Experimental Analysis of Hydraulic Jump at High Froude Numbers

Experimental Analysis of Hydraulic Jump at High Froude Numbers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental Analysis of Hydraulic Jump at High Froude Numbers Oguz Simsek, Mevlut Sami Akoz, Nazire Goksu Soydan Oksal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-213834/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The hydraulic jump is a rapid transition state from supercritical to subcritical flow that occurs commonly in rivers, prismatic channels and downstream of spillways. In this study, the characteristics of the hydraulic jump in a stilling basin downstream of the spillway chute channel with the slopes of α = 12 o and 30 o were investigated experimentally for different Froude numbers of incoming flow, Fr 1 = 7, 7.5, 8, 9, 10 and 12, and relative heights of sill in the range of 4 < h s /h 1 (S) < 13 (S relative height). In the experiments, in which velocity field measured by laser Doppler Anemometry, it was particularly focused on the effects of both different structural configuration and flow conditions on the hydraulic jump and energy dissipation ratio. Experimental measurements showed that the length of hydraulic jump and the roller zone increases with the decrease of the sill height for α = 12 o and 30 o . In addition, the length of the hydraulic jump and roller zone increased with decreasing Froude numbers. The turbulence intensity in the jump region was determined to be greater than the turbulence intensity in the region near the bottom of stilling basin. The turbulence intensity, in general, tended to decrease with decreasing Froude number. Civil Engineering Mechanical Engineering LDA Hydraulic jump Stilling basin Sill Turbulence Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 1. Introduction Hydraulic jump is a complex flow problem and surface discontinuity event that occurs during the transition from supercritical to subcritical regime in free surface flow, its occurrence depends on different hydraulic structures such as threshold, weir, sluice gate, base piers or stilling basin. These hydraulic structures cause the flow depth to increase and the flow to pass through the hydraulic jump process. The transition is an extremely turbulent flow associated with the development of large-scale turbulence, surface waves and spray, energy dissipation and air entrainment, and it is characterized by strong dissipative processes [ 1 ]. A hydraulic jump can serve many purposes. For example, to disperse flow energy to prevent bed erosion, to provide ventilation, or to facilitate mixing of chemicals used to purify water [ 2 ]. Stilling basins are designed and constructed to dissipate energy and thus reduce erosive power of the high velocity flow downstream of chute spillways. Geometric properties of a stilling basin depend upon the water depth and Froude number of the incoming flow and the required energy dissipation rate. Hydraulic jump stilling basins may include drops, expansion, sills, baffles, blocks and steps, typically used to decrease the basin length and stabilize the jump toe position [ 1 ]. An early study on the hydraulic jumps on the sloped channel was presented by Bakhmeteff, Matzke [ 3 ]. Kindsvater [ 4 ] classified jumps on the sloped channel according to their toe position relative to the channel bottom kink: A-jump for which the toe is at the kink, B-jump is the intermediate of A- and C-jumps, C-jump for which the end of roller is above the kink, and D-jump where the entire roller region is on the sloping channel. After the Kindvater's study, many studies have been conducted on these types of jumps [ 5 – 19 ]. Their main findings can be summarized as follows; (i) The energy dissipation rate decreases from A jump to D jump due to reduction in the force of hydraulic jump with the increasing tail water depth, (ii) The hydraulic characteristics of the classical jump and the A-jump are similar, (iii) Regarding the decay of bottom shear velocity, the sloping and the classical jumps are identical (iv) The roller lengths of C- and D-jumps are almost identical, (v) D-jumps are located between the classical jump and the classical wall jet as regards the decay of maximum forward velocity, (vi) The maximum bottom velocities and maximum surface velocities are near the side-walls and along the centerline of the channel, respectively. Peterka [ 20 ] summarized the extensive experimental tests conducted at the United States Bureau of Reclamation (USBR) and presented the general design rules of USBR-type stilling basins. Ohtsu et al. [ 21 ] experimentally measured the pressure distributions in the upstream and downstream region of the continuous and vertical sill in order to design a stilling basin for the purpose of creating a force hydraulic jump. By examining the flow characteristics passing over the sill, an experimental approach to the impulse force acting on the sill is proposed. Hager, Li [ 22 ], experimentally examined the effect of cross and uninterrupted sill on jump in a rectangular open channel. Based on the classical hydraulic jump results, they reported that the sill controlled hydraulic jump can be shown as an example of a disturbed classical hydraulic jump, especially in the case of the jump pattern. It was also reported that the erosion and hydraulic precision of the tail waterbed should be taken into consideration during the design process. Vittal, Al-Garni [ 23 ] presented a new method of design for the type USBR III stilling basin over a major range of discharges passing the spillway structure. The modified new basin is arranged in double rows of the single row of friction blocks in the USBR basin, to set up the velocity distribution of the subcritical flow after the hydraulic jump in the basin. Debabeche, Achour [ 24 ] investigated the effect of broad and thin crested sill on both the minimum-B jump and the sill-controlled jump under various inflow conditions in a horizontal symmetrical triangular open channel. Either a thin-crested or a broad-crested sill used to create hydraulic jumps, for the Froude numbers range from 2 to 10. The data obtained from a large number of experimental results were adapted to empirical relations to notice the effect of the inflow Froude number on the different parameters, for instance relative sill height and the non-dimensional toe position of the sill. Izadjoo, Shafai-Bejestan [ 25 ] experimentally investigated the effect of trapezoidal shape corrugated bed on flow characteristics of hydraulic jump for different Froude numbers and relative roughness. They found that corrugated bed, namely roughness, decreased the conjugate depth and hydraulic jump length 20% and 50% respectively. Ozbay [ 26 ] investigated the energy dissipation ratios of stepped, trapezoidal, T-shaped and wedge type baffle blocks placed the chute channels. From the experiments, it was found to be that the stepped baffle block type has slightly higher values of energy dissipation than the other baffle blocks tested in the study. Alikhani et al. [ 27 ] conducted an experiment to interpret the effects of a sill and position of sill on control of length and depth of a forced jump in stilling basin regardless of tailwater depth. The hydraulic properties of the jump measured in different discharges, compared with hydraulic properties of the classical hydraulic jump. As a result of the comparison, they determined that the sill had important effects on energy dissipation. They have developed a new relationship between parameters affecting hydraulic jump, such as sill height, sill distance, stilling basin length and sequential depth ratio. Hamidifar, Omid [ 28 ], conducted an experimental study to investigate the effect of a broad-crested sill on controlling the hydraulic jump formed in a horizontal and symmetrical triangular channel. Their results were compared with the previous experimental and theoretical studies and empirical equations were developed to predict the sequent depth ratio and the length of the jump and surface rollers. Ellayn, Sun [ 29 ] performed laboratory investigations to appraise the effect of a rough bed on hydraulic jump. The experiments were carried out using an artificially roughened bed with wedge-shaped baffle blocks for the Froude numbers in the range of 3.06 ≤ F 1 ≤ 10.95 and a relative bed roughness ranging 0.22 ≤ K R ≤1.4. They concluded that in the new stilling basin model, formed with the roughened bed with wedge-shaped baffle blocks, there was a reduction of 30–50% in the hydraulic jump length and 16.5–30% in the sequent depth compared to the smooth bed. Padulano et al. [ 30 ] carried out experimental studies on USBSR II type to figure out its hydraulic behavior and dissipation efficiency. The effect of a continuous, transverse sill on the hydraulic jump in a rectangular channel is experimentally analyzed by Hager, Li [ 22 ]. They classified submerged hydraulic jumps and hydraulic jump types from A-jump to spray. They provided the drag force and coefficients along with supposes of pressure extreme fluctuations. They also presented an assessment of dissipation efficiency for submerged and non-submerged jumps, and this assessment provided the opportunity to compare between different types of jump and classical hydraulic jump. Nandi et al. [ 31 ] experimentally and numerically investigated the hydraulic jump that occurs in flow conditions where the Froude number varies between 2.17 and 7 with three different channel base slopes. Using the data obtained as a result of experimental modeling, they developed an empirical formula to determine the location of the hydraulic jump by regression analysis. As a result of the study, the experimental results were compared with numerical model results and it was determined that the results were quite compatible with each other. Pourabdollah et al. [ 32 ], carried out experimentally free and submerged hydraulic jump in different stilling basins. The effects of different adverse slopes, rough beds and positive step heights on hydraulic jump characteristics in the range of 4.56 < Fr < 9.55 were investigated. They stated that the submerged depth ratio, lengths of the free and submerged hydraulic jumps are less than the classical hydraulic jump. When the studies in which hydraulic jump is controlled using the sill are examined, it has been observed that studies on determining the velocity field of hydraulic jump with LDA is not enough. The LDA system has a great advantage in obtaining the velocity and turbulence characteristics of the flow without any intervention in the flow field. In addition, in the past studies, the effect of sill height on energy dissipation ratio, turbulence intensity, the length of hydraulic jump and roller was not examined in the case of the same Froude number. In addition, while the hydraulic jump occurring after the sluice gate was examined in the previous studies, in this study the hydraulic jump is evaluated in the stilling basin after the spillway chute channel ([ 33 , 34 , 12 , 35 , 36 , 21 , 37 ]. For these reasons, this study has differences from the existing literature, and it is thought to contribute to the literature. It is well known that laser Doppler Anemometry (LDA) provides quantitative information on both instantaneous and time-averaged structures of the velocity field. Using instantaneous data, detailed information on the turbulent flow field could be obtained. In the event of forced hydraulic jump, the determination of the velocity field with the LDA will contribute. In addition, turbulence intensity, hydraulic jump length and characteristics of the roller region are determined in the case of different flows and sill heights. Some experimental study is available in the literature on the hydraulic jump; however, further experimental effort is needed either to confirm the previous findings or to provide new information for different experimental and structural conditions. The aim of the present study is to determine the hydraulic jump characteristics in a stilling basin downstream of the chute channel with different slopes for the Froude numbers in the range of 7 < Fr 1 < 12 and relative sill heights in the range of 4 < h s /h 1 < 13, where h s is the sill height and h 1 is the flow depth at the toe of jump. The results from the measured velocity fields by the LDA, turbulence intensity distributions, flow profiles, energy dissipation ratios and geometrical characteristics of hydraulic jump are presented to provide a detailed evaluation of the jump in a stilling basin. 2. Experimental Setup The experiments were performed in a rectangular, hydraulically smooth, side surfaces and base made of glass, horizontal stilling basin downstream of a spillway chute channel shown in Fig. 1 . The chute channel was 0.20 m, 0.20 m and 1.8 m wide, deep, long, respectively and the stilling basin was 0.20 m, 0.20 m and 1.50 m wide, deep, long, respectively. In the horizontal stilling basin, as shown in Fig. 1 , a single-row, continuous sill was installed. The slope of the downstream side of the sill was chosen as 1/2. The sill crest width (L s ) was determined as 2.5 cm for all sill heights. The width of the sill was the same as the width of the stilling basin. In order to control the depth of the water, a sluice gate was placed at the end of the stilling basin. The position and form of the hydraulic jump was controlled with the help of this gate. Two different spillway chute channel slopes, α = 30 o and 12 o , were used in the experiments. The velocity field was measured under three different flow conditions for each slope. The experiments were repeated for each sill height with different chute slopes. Experimental conditions are shown in Table 1 . In the table, h s sill height, h 1 is the water depth in the pre-jump section, V 1 is the average flow velocity in the pre-jump section, h 2 is the water depth of the cross-section after the jump, L b is the length of the stilling basin, Fr 1 is the Froude number of the incoming flow and α is slope angle of the chute channel. As can be seen from Table 1 , when the Froude number is 12 and 10, type A and free hydraulic jump occurs, while under other flow and sill conditions, type B and submerged hydraulic jump occurs. Table 1 Experimental conditions Fr 1 V 1 (m/s) h s /h 1 h 2 /h 1 L b /h 1 Jump Type α = 30 o 12.0 2.48 9 8.60 89 A/Free 8 8.00 97 A/Free 7 7.60 100 A/Free 10.0 1.85 11 6.75 100 A/Free 10 6.45 100 A/Free 9 6.10 100 A/Free 9.0 1.57 13 6.45 103 B/Sub. 11 6.25 116 B/Sub. 10 6.10 110 B/Sub. α = 12 o 8.0 0.70 6 9.70 71 B/Sub. 5 8.80 79 B/Sub. 4 8.30 126 B/Sub. 7.5 0.55 7 8.80 80 B/Sub. 6 8.10 84 B/Sub. 5 7.75 91 B/Sub. 7.0 0.50 8 8.25 80 B/Sub. 7 7.70 80 B/Sub. 6 6.70 90 B/Sub. In the experiments, the flow velocities in the channel axis were measured with Laser Doppler Anemometer (LDA) and recorded with a Dantec LDA 62N04 flow explorer 1D high-power system, including a burst spectrum analyzer (BSA) F30 processor and integrated photo multiplier unit with BSA flow software. Laser output is supplied by operating in a wavelength of 660 nm. Beam spacing is 60 mm, and the measurable velocity fluctuation varies from 0.7 µm = s to 4.6 mm/s. The time-averaged velocity at a point was detected by postprocessing of the measured instantaneous velocities. Some turbulence characteristics of the flow can also be determined from the time series containing instantaneous velocity values. Using LDA system, the measurement time is adjusted to obtain flow parameters such as turbulence and velocity over a certain time interval or by using the number of measured data. Depending on the properties of the flow at the measurement point, the frequency, and the measured data validation levels of the LDA system can vary. Since these data are seen insufficient, the measured turbulence and velocity values were not used especially in the roller region. The LDA performs instantaneous velocity measurements with ± 1% accuracy within 95% confidence interval. The postprocessing of the measured instantaneous velocities are carried out by BSA Flow software. This software includes both classic and advanced Spectrum algorithms. With the advanced Spectrum algorithm, turbulence spectra can be correctly estimated to frequencies near the mean data rate. The upper frequency limit is thus higher than that of the classic Spectrum algorithm, which shows low-pass filtering behavior, with a cut-off frequency equal to half the mean data rate. This process is done automatically by the BSA Flow software. The discharge and free surface level were measured by ultrasonic flow meter and limnimeter, respectively. As a result of the LDA measurement, the flow average velocity obtained along the depth is compared. In addition, discharge was measured with the help of a 60x60x20 chamber at the end of the channel. Thus, LDA velocity values were verified by 2 different methods. The relative sill height at the same Froude numbers has not clearly effect on the variation of relative length of the hydraulic jump, L j /h 1 , and the relative roller zone, L r /h 1 . The change of h s / h 1 ratio according to the number of Fr 1 is given in Fig. 2 . When the figure is examined, it is seen that the previous studies is not contain the cases where the h s / h 1 ratio is greater than 8. Also, it is seen that the h s / h 1 ratio used for 6 < Fr 1 < 8 in the current studies, has not been addressed in the literature. 3. Results And Discussions The experimental velocity profiles, free surface flow profiles, geometrical properties of hydraulic jump, turbulence intensity distributions and energy dissipation rates for different flow and sill conditions were presented. The velocities at the chute channel and the stilling basin were measured parallel to the bottom of the channel base with LDA system. The instantaneous velocities in the channel middle axis are measured and recorded with LDA and the time-averaged velocity at a point was determined by postprocessing of the measured instantaneous velocities. The Froude numbers of incoming flows for different flow and sill conditions were calculated from the velocity measurements at chute channel. The velocities at the region where air mixture is dense could not be measured with LDA. 3.1. Velocity Profiles The streamwise velocity profiles at various sections of the stilling basin were presented in Figs. 3 – 8 for the ranges of h s /h 1 = 4 −13, chute channel slopes, α = 30 o and α = 12 o ; Froude numbers, Fr = 7, 7.5, 8, 9, 10, 12. The velocity profiles under the circulatory flow region are similar to those of plane turbulent wall jet. The streamwise velocities increase from zero at the stilling basin wall to a maximum value at y = δ 0 , which is thickness of boundary layer. As can be seen from the figures, the boundary layer thickness increases with the distance from the entrance of stilling basin. The jet layer extends up to the inflexion point (change of slope of streamwise velocity, du 2 /dy 2 = 0), which is the lower boundary of the roller region. A roller region that is divided by the line u = 0 into inner- and outer-regions of circulatory flow takes place above the wall-jet flow layer. Momentum exchange occurs through the null streamwise velocity line within the circulatory flow layer (Dey et al. [ 38 ]. It can also be seen from the figures of the velocity profiles that the streamwise velocity, in general, tends to decrease with increasing Froude number. On the other hand, the streamwise velocity values are in a decreasing trend with increasing sill height. The maximum streamwise velocity occurs immediately upon entering the stilling basin for all the experiments and the intensity of the maximum streamwise velocity decreases as it moves downstream. It is clearly seen from the Figures that the peak velocity values in the stilling basin for the chute channel slopes, α = 12 o are higher than those of the α = 30 o . The point at which streamwise velocity attained its peak value slightly shifts to toward free surface as moving in the streamwise direction. At the same Fr numbers, the maximum streamwise velocity, in general, decreases with the increase of the sill height. The values of peak velocity decrease as the Froude number are decreased at the same height of sill for both α = 12 o and α = 30 o . The rate of decay of maximum wall- jet velocity for α = 30 o is slightly greater than that for α = 12 o . The mean rate of the decay of the maximum values is approximately 80% for all experiments. The thickness of the roller region increases with increasing both Froude number and sill height. The thickness of the roller zone gradually decreases as it moves downstream. The flow separation from the bed surface of the basin occurs in the just upstream of the sill. These boundary layer separations result from the increased pressure gradient and the inability of the flow to follow the geometric shape of the sill structure. The starting point of separation is located approximately at 0.5h s from the sill structure and the thickness of the separation region is approximately 0.15h s for all experiments. Boundary layer separation on the crest of sill and channel bottom downstream of the sill occurs for in almost all cases. In the same flow condition, the density of the air mixture in the hydraulic jump increases as the sill height decreases. In addition, the density of the air mixture increases with increasing inflow Froude number. The height of the side walls of the stilling basin is directly associated with the depth of water (h 2 ) formed after hydraulic jump. The high enough side wall height prevents effective hydraulic jumping, but also plays a role in ensuring the safety of structures and riverbed in the downstream region. For α = 12 o and 30 o chute channel slopes, experimental water surface profiles obtained using limnimeter are obtained for the different Froude numbers (Fr 1 = 12, 10, 9, 8, 7.5 and 7) and relative sill heights, h s /h 1 ranging from 4 to 13. The flow profiles in the jump zone were determined on average at the entrance of the stilling basin, due to the dynamic nature of the hydraulic jump and the dense air mixture. The figures show that with the decrease in the sill height, the amount of swelling that occurs at the upstream of the water depth and sill structure does not decrease. There is almost a uniform depth in the downstream region of the sill. Another result is that with the decrease in the Froude number, the water depth after the hydraulic jump is reduced. For different sill heights and Froude numbers, in different sections of the stilling basin, the ratio of the maximum horizontal velocity component obtained along the water depth to the mean flow velocity before the hydraulic jump, the change of the cross-section distance according to the depth before the hydraulic jump is given in Fig. 9 . It can be seen from the figure that the maximum value of u max / V 1 decreases with increasing sill height. For all sill heights and Froude numbers, it is determined that when the x/y 1 value is about 50, the jet flow loses its effect. Namely, the hydraulic jump is about to be completed. It is seen that the u max / V 1 value increases again in the region close to the sill for all the heights of sill and Froude numbers. 3.2. Geometric Properties of Hydraulic Jumps Figure 10 gives the geometric properties of the hydraulic jump. The lengths of the hydraulic jump and roller zone are determined by the large amount of color experiment. In this case, the experiments of hydraulic jump recorded with high resolution camera. The lengths of hydraulic jump and roller region are determined from the videos recorded. In addition, the beginning and the end section of the hydraulic jump and roller region are controlled and verified by the measurement of the velocity profiles by using LDA. In the case of the same Froude number, L j /h 1 and L r /h 1 ratios decrease with the increase of the relative sill height. In addition, as the slope of the chute channel changes from 12 o to 30 o , the L j /h 1 and L r /h 1 ratios obtained for different Froude numbers are highly decreases. In cases chute channel slope is α = 12 o , the ratio of L j /h 1 and L r /h 1 generally decreases with the decrease of the Froude number, while in the case of α = 30 o , the ratios of L j /h 1 and L r /h 1 increases as the Froude number increases due to the change of hydraulic jump type is from A type to B type, are given in the Table 1 . The comparison of the change of the L r / h 1 according to the Froude number with the results of previous studies is given in Fig. 11 [ 39 – 41 , 37 , 42 ]. While the results of this study are found to be consistent with the results of Kucukali, Chanson [ 39 ], there is a slight difference in the results of the Froude numbers 11 and 12. The discrepancy between the present study and previous studies is thought to be due to the creation of the hydraulic jump. 3.3 Turbulence Intensity The flow has low velocity in the upstream of spillway (subcritical region) passes through the structure crest (the critical depth) and reaches high velocities on the chute channel (the super critical region). This flow, has a very high energy, is subjected to hydraulic jump to create excessive turbulence and de-energized without damaging the structure and riverbed. The LDA measures the instantaneous velocity values at the point where the velocity of the flow is determined and gives the opportunity to obtain the average velocity and velocity deviations related to the flow by using these values. The turbulence intensity (I) is calculated as given in Eq. 1 with the help of instantaneous point velocities in the flow region obtained by one-dimensional LDA used in the experiments: $$I=\frac{{\sqrt {\overline {{{{u^{\prime}}^{^{2}}}}} } }}{{\bar {u}}}$$ 1 where and refers to the turbulence velocity deviation and the mean velocity value at the measured point, respectively. Figures 12-15 show that the wall-normal profiles of streamwise turbulence intensities at the different section of the stilling basin for Froude numbers and relative sill heights used in the present study. At the entrance to the stilling basin, the streamwise turbulence intensities first increase rapidly in the near-wall region and reach at a peak value then decreases and then increases again as it moves towards the free surface. The value of maximum streamwise turbulence intensity is higher than that of the free surface in the entrance region of the basin. The peak values of the turbulence intensities take place only in the roller region of the jump as it moves towards the downstream in the hydraulic jump region. In the roller region, the maximum streamwise turbulence intensity occurs around the line u=0, where momentum exchange occurs. When the jump zone ends, the peak values of the streamwise turbulence intensity take place in the near-wall region as in the classical open channel flow. The peak values of streamwise turbulence intensity close to bottom take place in the region 0.003<y/d 0 <0.8, y is wall-normal ordinate and d 0 is vertical distance where u=u max . When the maximum values were compared, it was observed that the turbulent intensity values in the roller region were larger than those close to the bottom. It can be said from the experimental measurements that the streamwise turbulence intensity, in general, tends to increase with increasing Froude number. α=12 o creates larger turbulence intensities at the entrance to the stilling base compared to α=30 o . No clear influences of the relative sill height on the variation of the streamwise turbulence intensities. 3.4 Energy Dissipation Ratio in Hydraulic Jump The water discharged over a spillway crest attains a very high kinetic energy and velocity at the end of spillway chute channel. This high velocity flow may cause serious scour and erosion of riverbed downstream. Hydraulic jumps are used for the reduction of energy and velocity downstream of a spillway chute. The hydraulic jump can be seen in various forms depending on the pre-jump flow conditions. The energy losses can reach up to 65–85% depending on the Froude number of the incoming flow in the classical jump as in the jump occurs after the sluice gate (jump on the flat base). On the other hand, the energy losses in the hydraulic jumps occurring in the stilling basin at the downstream region of the spillway chute channel are slightly lower. The energy dissipated in the jump is represented by the loss of specific energy: $${E}_{L}={E}_{1}-{E}_{2}=\left({h}_{1}+\frac{{V}_{1}^{2}}{2g}\right)-\left({h}_{2}+\frac{{V}_{2}^{2}}{2g}\right)$$ 2 Figure 16 -a shows the energy losses in the hydraulic jump calculated using Eq. ( 2 ) for different Froude numbers of incoming flow and chute slope of α = 12° and 30°. It is clearly seen from the figure that dissipated energy considerably increases because of the stronger jump when the Froude number is increased for both α = 12° and 30°. The dissipation energy rate is increasing with Froude number at a faster rate for α = 12° than α = 30°. In Fig. 20-b, the changes of energy dissipation ratio according to h s /h 1 are presented for the chute channel slopes α = 30 o and 12 o . The dissipated energy decreases when the relative sill height, h s /h 1 , is increased for both α = 12° and 30°. Table 2 shows the ratios of dissipated energy at the hydraulic jump for different sill heights and Froude numbers. It is seen from the table that the maximum dissipated energy rate occurs for Fr 1 = 12 and h s /h 1 = 7. Table 2. Energy dissipation ratios at the hydraulic jump for different structure and flow conditions α = 30 o α = 12 o Fr 1 h s /h 1 E L /E 1 (%) Fr 1 h s /h 1 E L /E 1 (%) 12.0 9 73 8.0 6 57 8 74 5 61 7 76 4 63 10.0 11 62 7.5 7 46 10 64 6 50 9 65 5 52 9.0 13 50 7.0 8 36 11 51 7 40 10 52 6 48 In addition, in Fig. 17 , the changes of energy dissipation ratio according to h 1 /h 2 are presented for α = 30 o and 12 o . As can be seen from the figures, the energy losses in the hydraulic jump increase with increasing Froude number at the same ratio of h 1 /h 2 . Under conditions where the Froude number is constant, the energy loss decreases with the reduction of the h 2 / h 1 ratio. The energy dissipation rate in the hydraulic jump in the downstream region of spillway is less than the classical hydraulic jump after the sluice gate. In the cases where the Fr 1 = 12, 10 and 9, the energy dissipation rate for h s = 4 cm is 72.6, 61.9 and 49.6%, the energy dissipation rate for h s =3.5 cm is 74.4%, 63.5 and 51.2, respectively, for h s = 3 cm this ratio is 75.7, 65.4 and 52.3%, respectively. Figure 18 shows the comparison of the energy dissipation rate according to the Froude number with Fathi-Moghadam et al. [ 34 ]. The energy dissipation rate obtained for Fr 1 = 12 is quite similar to the results obtained by Fathi-Moghadam et al. [ 34 ]. Besides, for Fr 1 = 8, there is about 10% difference in energy dissipation rate obtained with the same h s / h 1 ratio as the results obtained by Fathi-Moghadam et al. [ 34 ]. Due to the submerged hydraulic jump occurring in the downstream region of the spillway, the energy dissipation rate obtained in this study is less for other flow conditions. In addition, the tail water depth influences reducing the energy dissipation rates. 4. Conclusions In this study, experimental measurements were performed by using different Froude numbers and sill heights to determine the hydraulic jump characteristics in a stilling basin downstream of the spillway chute channel. From the measured velocity fields by LDA, the effects of Froude numbers and sill heights on hydraulic jump characteristics were investigated. The following results were found: Results show that the maximum streamwise velocity occurs immediately upon entering the stilling basin for all the experiments and the intensity of the maximum streamwise velocity decreases as it moves downstream. At the same Fr numbers, the maximum streamwise velocity, in general, decreases with the increase of the sill height. The values of peak velocity decrease as the Froude number are decreased at the same height of sill for both chute channel slope α = 12 o and α = 30 o . Furthermore, the maximum value of u max / V 1 decreases with increasing sill height. For all sill heights and Froude numbers, it is determined that when the x/y 1 value is about 50, the jet flow loses its effect. Namely, the hydraulic jump is about to be completed. The relative length of the hydraulic jump and the relative roller zone increase with the decrease of the relative sill height for chute channel slope α = 30 o and α = 12 o . The experimental data show that the length of the roller region and hydraulic jump for α = 30 o are greater than those of α = 12 o . The thickness of the roller region increases with increasing both Froude number and sill height. The thickness of the roller zone gradually decreases as it moves downstream in the stilling basin. It can be concluded that the relative sill height at the same Froude numbers has not clearly effect on the variation of relative length of the hydraulic jump, L j /h 1 , and the relative roller zone, L r /h 1 . When the maximum values were compared, it was observed that the turbulent intensity values in the roller region were larger than those close to the bottom. In the roller region, the maximum streamwise turbulence intensity occurs around the line u = 0, where momentum exchange occurs. Energy dissipation considerably increases because of the stronger jump as the Froude number is increased for both α = 12° and 30°. The dissipated energy in the stilling basin decreases when the relative sill height is increased for both α = 12° and 30°. In addition, the tail water depth has an effect on reducing the energy dissipation rates. Declarations DECLARATION OF COMPETING INTEREST The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from the corresponding author upon reasonable request. Author statement Oguz SIMSEK: Conceptualization, Methodology, Validation, Formal analysis Investigation, Resources, Writing – original draft, Writing – review & editing. M. Sami AKOZ: Conceptualization, Methodology, Validation, Investigation, Writing – original draft, Writing – review & editing, Supervision . N. Goksu SOYDAN OKSAL: Methodology, Investigation, Formal analysis, Writing – review & editing. Acknowledgement and Funding Information Not Applicable References Chanson H (2015) Energy dissipation in hydraulic structures. CRC Press Gumus V, Simsek O, Soydan NG, Akoz MS, Kirkgoz MS (2016) Numerical modeling of submerged hydraulic jump from a sluice gate. Journal of irrigation drainage engineering 142(1):04015037 Bakhmeteff B, Matzke A (1938) The hydraulic jump in sloped channels. Trans ASME 60 (HYD-60-l):111–118 Kindsvater CE (1944) The hydraulic jump in sloping channels. Trans ASCE 109:1107–1154 Bradley J, Peterka A (1957) The hydraulic design of stilling basins: hydraulic jumps on a horizontal apron (basin i). J Hydraulics Div 83(5):1–24 Bunyan J (1958) SOME ASPECTS OF THE DESIGN OF HYDRAULIC STRUCTURES IN ALLUVIUM. Proceedings of the Institution of Civil Engineers 10 (2):145–162 Smith DW, Walker JH (1959) Skin-friction measurements in incompressible flow. vol 4231. National Advisory Committee for Aeronautics Rao N, Rajaratnam N (1963) The submerged hydraulic jump. J Hydraulics Div 89(1):139–162 Mahmood K (1964) Effect of apron slope on hydraulic jump performance. University of Washington Wielogorski J, Wilson E (1970) Non-dimensional profile area coefficients for hydraulic jump in sloping rectangular channels. WATER POWER 22(4):144–150, APR 1970 7 P, 13 FIG, 2 TAB, 11 REF Hari VM (1973) Plane Jet on Sloping Floors under Finite Submergence. J Hydraulics Div 99(9):1449–1460 Ohtsu I, Yasuda Y (1991) Hydraulic jump in sloping channels. J Hydraul Eng 117(7):905–921 Rajaratnam N, Murahari V (1974) FLOW CHARACTERISTICS OF SLOPING CHANNEL JUMPS. J Hydraulics Div 100(HY6):731–740 Mikhalev M, An HT (1976) Kinematic characteristics of a hydraulic jump on a sloping apron. Hydrotechnical Construction 10(7):686–690 Hager WH (1988) B-jump in sloping channel. J Hydraul Res 26(5):539–558 Sene K, Thomas N, Goldring B (1989) Planar plunge-zone flow patterns and entrained bubble transport. J Hydraul Res 27(3):363–383 Kawagoshi N, Hager W (1990) B-jump in sloping channel, II. J Hydraul Res 28(4):461–480 Chern M-J, Vaziri N (2020) Effect of Porous Media on Hydraulic Jump Characteristics by Using Smooth Particle Hydrodynamics Method. International Journal of Civil Engineering 18(3):367–379 Kazemi F, Khodashenas SR, Sarkardeh H (2016) Experimental study of pressure fluctuation in stilling basins. International Journal of Civil Engineering 14(1):13–21 Peterka A (1958) Hydraulic design of stilling basins and energy dissipaters engineering monograph No. 25. US Bureau of Reclamation, Denver Colorado Ohtsu I, Yasuda Y, Yamanaka Y (1991) Drag on vertical sill of forced jump. J Hydraul Res 29(1):29–47 Hager WH, Li D (1992) Sill-controlled energy dissipator. J Hydraul Res 30(2):165–181 Vittal N, Al-Garni AM (1992) Modified type III stilling basin-new method of design. J Hydraul Res 30(4):485–498 Debabeche M, Achour B (2007) Effect of sill in the hydraulic jump in a triangular channel/Effet du seuil sur le ressaut hydraulique dans un canal triangulaire. J Hydraul Res 45(1):135–139 Izadjoo F, Shafai-Bejestan M (2007) Corrugated bed hydraulic jump stilling basin. Journal of Applied Sciences 7(8):1164–1169 Ozbay O (2009) Şüt kanallarına yerleştirilen farklı tip enerji kırıcı blokların incelenmesi/An investigation of energy dissipation ratios of different type energy dissipator blocks in chute channels Alikhani A, Behrozi-Rad R, Fathi-Moghadam M (2010) Hydraulic jump in stilling basin with vertical end sill. International journal of physical sciences 5(1):25–29 Hamidifar H, Omid M (2011) Using a broad crested sill to control hydraulic jump in a triangular channel. J Civil Eng (IEB) 39(2):103–110 Ellayn AF, Sun Z-l (2012) Hydraulic jump basins with wedge-shaped baffles. Journal of Zhejiang University SCIENCE A 13(7):519–525 Padulano R, Fecarotta O, Del Giudice G, Carravetta A (2017) Hydraulic design of a USBR Type II stilling basin. J Irrig Drain Eng 143(5):04017001 Nandi B, Das S, Mazumdar A, Experimental Analysis and Numerical Simulation of Hydraulic Jump. In: IOP Conference Series: Earth and Environmental Science (2020) vol 1. IOP Publishing, p 012024 Pourabdollah N, Heidarpour M, Abedi Koupai J Characteristics of free and submerged hydraulic jumps in different stilling basins. In: Proceedings of the Institution of Civil Engineers-Water Management, 2020. vol 3. Thomas Telford Ltd, pp 121–131 Rand W (1965) Flow over a vertical sill in an open channel. J Hydraulics Div 91(4):97–121 Fathi-Moghadam M, Kiani S, Asiaban P, Behrozi-Rad R (2017) Modeling of Perforated Sill-Controlled Hydraulic Jump. International Journal of Civil Engineering 15(4):689–695 Karki K, Kumar S (1992) DRAG ON VERTICAL SILL OF FORCED JUMP-DISCUSSION. JOURNAL OF HYDRAULIC RESEARCH 30 (2):280–284 Ohtsu I, Yasuda Y, Hashiba H (1996) Incipient jump conditions for flows over a vertical sill. J Hydraul Eng 122(8):465–469 Hager WH, Bremen R, Kawagoshi N (1990) Classical hydraulic jump: length of roller. J Hydraul Res 28(5):591–608 Dey S, Nath TK, Bose SK (2010) Fully rough submerged plane wall-jets. J Hydro-Environ Res 4(4):301–316 Kucukali S, Chanson H (2008) Turbulence measurements in the bubbly flow region of hydraulic jumps. Exp Thermal Fluid Sci 33(1):41–53 Murzyn F, Chanson H (2008) Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps. Exp Fluids 45(3):513–521 Murzyn F, Chanson H (2009) Free-surface fluctuations in hydraulic jumps: Experimental observations. Exp Thermal Fluid Sci 33(7):1055–1064 Wang H, Chanson H (2015) Experimental study of turbulent fluctuations in hydraulic jumps. J Hydraul Eng 141(7):04015010 Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-213834","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":11363974,"identity":"27bb316d-662a-4c2a-adb9-f8d40f060a50","order_by":0,"name":"Oguz Simsek","email":"","orcid":"","institution":"Harran University: Harran Universitesi","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Oguz","middleName":"","lastName":"Simsek","suffix":""},{"id":11363975,"identity":"e3429e92-3a56-412f-bb18-61dc11ed06b7","order_by":1,"name":"Mevlut Sami Akoz","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYLCCBCBkYG8AsgwsSNHCcwCkRYIEexgkEkAMIrTo9h9+uuFBTZqc/MznVzf8KJBg4G/vTsCrxexGmtmNhGM5xoyzc8pu9gAdJnHm7AYCWoAoga0isVk6J+0GD1CLgUQuAS3nj3+7kfCvIrFN8kzazT9EaTmQY3YjsS0nsUeC/dht4my5kVN2I7EvzViCJ4fttoyBBA9hv5w/vu3mj2/JcvLtx5/dfPPHRo6/vRe/FiTAYwAmiVUOAuwPSFE9CkbBKBgFIwgAAHZxStUOEr4wAAAAAElFTkSuQmCC","orcid":"","institution":"Cukurova University: Cukurova Universitesi","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Mevlut","middleName":"Sami","lastName":"Akoz","suffix":""},{"id":11363976,"identity":"0061227a-4029-456b-82f3-3085a9826ad1","order_by":2,"name":"Nazire Goksu Soydan Oksal","email":"","orcid":"","institution":"Mersin University: Mersin Universitesi","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nazire","middleName":"Goksu 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2","display":"","copyAsset":false,"role":"figure","size":123306,"visible":true,"origin":"","legend":"The comparison of the change of hs / h1 ratio according to Fr1 with previous studies","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/5d7da6bf0ddc446a4460b7bb.png"},{"id":6228872,"identity":"a30851fa-db37-49f3-8077-dabdba6f586a","added_by":"auto","created_at":"2021-02-22 23:55:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":193017,"visible":true,"origin":"","legend":"Streamwise velocity profiles at different sections in the stilling basin for Fr1=12 and hs /h1 =7, 8, 9.","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/bda5474bd9c50aec0bd83e25.png"},{"id":6230319,"identity":"70aacacc-60ce-4bbf-9c77-84e568109bd2","added_by":"auto","created_at":"2021-02-23 00:04:11","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":208540,"visible":true,"origin":"","legend":"Streamwise velocity profiles at different sections in the stilling basin for Fr1=10 and hs /h1 =9, 10, 11.","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/d21a4877ca6bb4ce7ae837a0.png"},{"id":6228221,"identity":"2b7521f1-4ce9-4e80-a3e6-268e4456c66c","added_by":"auto","created_at":"2021-02-22 23:52:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":208624,"visible":true,"origin":"","legend":"Streamwise velocity profiles at different sections in the stilling basin for Fr1=9 and hs /h1 =10, 11, 13.","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/293ee33e2ee5b6f3c036d6ab.png"},{"id":6229445,"identity":"7cb6e99c-660f-444f-ae32-ddf9f3f4f6f4","added_by":"auto","created_at":"2021-02-22 23:58:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":189833,"visible":true,"origin":"","legend":"Streamwise velocity profiles at different sections in the stilling basin for Fr1=8 and hs /h1 =4, 5, 6.","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/205afadcc28b70fbae8da561.png"},{"id":6229446,"identity":"2145f2c4-2787-4551-8a72-26cf54568c90","added_by":"auto","created_at":"2021-02-22 23:58:11","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":192554,"visible":true,"origin":"","legend":"Streamwise velocity profiles at different sections in the stilling basin for Fr1=7.5 and hs /h1 =5, 6, 7.","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/517efb8c3dc326c66d58d1cf.png"},{"id":6228874,"identity":"4537f256-2c04-40cb-94fd-6bdd69ab47f6","added_by":"auto","created_at":"2021-02-22 23:55:11","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":198381,"visible":true,"origin":"","legend":"Streamwise velocity profiles at different sections in the stilling basin for Fr1=7 and hs /h1 = 6, 7, 8.","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/affd1cf95fd0a286677f6c39.png"},{"id":6228878,"identity":"1f939974-aaac-4890-bc50-380a8a94201d","added_by":"auto","created_at":"2021-02-22 23:55:12","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":174781,"visible":true,"origin":"","legend":"umax/V1 according to x/y1 for the different height of sill and Froude numbers","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/bc86c1cd94516e14c95414ad.png"},{"id":6228219,"identity":"45139c34-90d0-4101-8328-a0757231f70b","added_by":"auto","created_at":"2021-02-22 23:52:11","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":77259,"visible":true,"origin":"","legend":"Lj /h1 and Lr/h1 according to hs/h1 for the different Froude numbers","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/207147f75794067449876392.png"},{"id":6229824,"identity":"c59614d1-5753-487c-b720-38bd26b50b22","added_by":"auto","created_at":"2021-02-23 00:01:11","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":118657,"visible":true,"origin":"","legend":"The comparison of the change of the Lr / h1 according to the Fr1 with previous studies ","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/85119d3239d02d2e4ec1fb86.png"},{"id":6228875,"identity":"ecf18862-3ef6-4e99-b294-e22bedbac6bd","added_by":"auto","created_at":"2021-02-22 23:55:12","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":148256,"visible":true,"origin":"","legend":"Turbulence intensity for Fr1=12, a) hs/ h1 =7, b) hs/ h1 =8 and c) hs/ h1 =9, α=30°.","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/741489d9873702bcb78f7c7b.png"},{"id":6228882,"identity":"97f2d644-c047-4254-8e02-532b5cd4179a","added_by":"auto","created_at":"2021-02-22 23:55:12","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":144922,"visible":true,"origin":"","legend":"Turbulence intensity for Fr1=9, a) hs/ h1 =10, b) hs/ h1 =11 and c) hs/ h1 =13, α=30°","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/f9e67d5eba32f27ebf76107a.png"},{"id":6228877,"identity":"199fe692-0d99-40f1-930e-d385b7d1faba","added_by":"auto","created_at":"2021-02-22 23:55:12","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":147589,"visible":true,"origin":"","legend":"Turbulence intensity for Fr1=8, a) hs/ h1 =4, b) hs/ h1 =5 and c) hs/ h1 =6, α=12°","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/ea73de4ccd180eac246929bf.png"},{"id":6228222,"identity":"edd616b9-bb4d-4744-87b0-6f8ba80c1737","added_by":"auto","created_at":"2021-02-22 23:52:12","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":162756,"visible":true,"origin":"","legend":"Turbulence intensity for Fr1=7, a) hs/ h1 =6, b) hs/ h1 =7 and c) hs/ h1 =8, α=12°","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/d4cb7dd1e445747412a469af.png"},{"id":6228223,"identity":"7a699b70-8e49-44bf-9ea7-ff27592336a5","added_by":"auto","created_at":"2021-02-22 23:52:12","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":64448,"visible":true,"origin":"","legend":"Energy dissipation ratio according to Fr1 and hs/h1.","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/867d481f16b50adbd3d79a26.png"},{"id":6229449,"identity":"a7a87e52-9033-41de-9a6c-49d14901877c","added_by":"auto","created_at":"2021-02-22 23:58:12","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":70535,"visible":true,"origin":"","legend":"Energy dissipation ratio according to h2/h1.","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/d06d5e32981cac6ed3a77e7e.png"},{"id":6228227,"identity":"7f8b87ab-23f2-45f5-bc1e-6d7f19cdbaaf","added_by":"auto","created_at":"2021-02-22 23:52:12","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":56156,"visible":true,"origin":"","legend":"The comparison of the EL/E1 according to the Fr1 with Fathi-Moghadam et al. [34]","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/3ca8d3af7f48e416e436b309.png"},{"id":13669230,"identity":"ca37335a-fbe6-4d47-bc97-aa4924449915","added_by":"auto","created_at":"2021-09-17 10:59:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2643694,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-213834/v1/886cdc94-9dbb-42cc-b0e6-0c7575634e5f.pdf"}],"financialInterests":"","formattedTitle":"Experimental Analysis of Hydraulic Jump at High Froude Numbers","fulltext":[{"header":"1. Introduction","content":" \u003cp\u003eHydraulic jump is a complex flow problem and surface discontinuity event that occurs during the transition from supercritical to subcritical regime in free surface flow, its occurrence depends on different hydraulic structures such as threshold, weir, sluice gate, base piers or stilling basin. These hydraulic structures cause the flow depth to increase and the flow to pass through the hydraulic jump process. The transition is an extremely turbulent flow associated with the development of large-scale turbulence, surface waves and spray, energy dissipation and air entrainment, and it is characterized by strong dissipative processes [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. A hydraulic jump can serve many purposes. For example, to disperse flow energy to prevent bed erosion, to provide ventilation, or to facilitate mixing of chemicals used to purify water [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eStilling basins are designed and constructed to dissipate energy and thus reduce erosive power of the high velocity flow downstream of chute spillways. Geometric properties of a stilling basin depend upon the water depth and Froude number of the incoming flow and the required energy dissipation rate. Hydraulic jump stilling basins may include drops, expansion, sills, baffles, blocks and steps, typically used to decrease the basin length and stabilize the jump toe position [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAn early study on the hydraulic jumps on the sloped channel was presented by Bakhmeteff, Matzke [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Kindsvater [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] classified jumps on the sloped channel according to their toe position relative to the channel bottom kink: A-jump for which the toe is at the kink, B-jump is the intermediate of A- and C-jumps, C-jump for which the end of roller is above the kink, and D-jump where the entire roller region is on the sloping channel. After the Kindvater's study, many studies have been conducted on these types of jumps [\u003cspan additionalcitationids=\"CR6 CR7 CR8 CR9 CR10 CR11 CR12 CR13 CR14 CR15 CR16 CR17 CR18\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Their main findings can be summarized as follows; (i) The energy dissipation rate decreases from A jump to D jump due to reduction in the force of hydraulic jump with the increasing tail water depth, (ii) The hydraulic characteristics of the classical jump and the A-jump are similar, (iii) Regarding the decay of bottom shear velocity, the sloping and the classical jumps are identical (iv) The roller lengths of C- and D-jumps are almost identical, (v) D-jumps are located between the classical jump and the classical wall jet as regards the decay of maximum forward velocity, (vi) The maximum bottom velocities and maximum surface velocities are near the side-walls and along the centerline of the channel, respectively. Peterka [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] summarized the extensive experimental tests conducted at the United States Bureau of Reclamation (USBR) and presented the general design rules of USBR-type stilling basins. Ohtsu et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] experimentally measured the pressure distributions in the upstream and downstream region of the continuous and vertical sill in order to design a stilling basin for the purpose of creating a force hydraulic jump. By examining the flow characteristics passing over the sill, an experimental approach to the impulse force acting on the sill is proposed. Hager, Li [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], experimentally examined the effect of cross and uninterrupted sill on jump in a rectangular open channel. Based on the classical hydraulic jump results, they reported that the sill controlled hydraulic jump can be shown as an example of a disturbed classical hydraulic jump, especially in the case of the jump pattern. It was also reported that the erosion and hydraulic precision of the tail waterbed should be taken into consideration during the design process. Vittal, Al-Garni [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] presented a new method of design for the type USBR III stilling basin over a major range of discharges passing the spillway structure. The modified new basin is arranged in double rows of the single row of friction blocks in the USBR basin, to set up the velocity distribution of the subcritical flow after the hydraulic jump in the basin. Debabeche, Achour [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] investigated the effect of broad and thin crested sill on both the minimum-B jump and the sill-controlled jump under various inflow conditions in a horizontal symmetrical triangular open channel. Either a thin-crested or a broad-crested sill used to create hydraulic jumps, for the Froude numbers range from 2 to 10. The data obtained from a large number of experimental results were adapted to empirical relations to notice the effect of the inflow Froude number on the different parameters, for instance relative sill height and the non-dimensional toe position of the sill. Izadjoo, Shafai-Bejestan [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] experimentally investigated the effect of trapezoidal shape corrugated bed on flow characteristics of hydraulic jump for different Froude numbers and relative roughness. They found that corrugated bed, namely roughness, decreased the conjugate depth and hydraulic jump length 20% and 50% respectively. Ozbay [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] investigated the energy dissipation ratios of stepped, trapezoidal, T-shaped and wedge type baffle blocks placed the chute channels. From the experiments, it was found to be that the stepped baffle block type has slightly higher values of energy dissipation than the other baffle blocks tested in the study. Alikhani et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] conducted an experiment to interpret the effects of a sill and position of sill on control of length and depth of a forced jump in stilling basin regardless of tailwater depth. The hydraulic properties of the jump measured in different discharges, compared with hydraulic properties of the classical hydraulic jump. As a result of the comparison, they determined that the sill had important effects on energy dissipation. They have developed a new relationship between parameters affecting hydraulic jump, such as sill height, sill distance, stilling basin length and sequential depth ratio. Hamidifar, Omid [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], conducted an experimental study to investigate the effect of a broad-crested sill on controlling the hydraulic jump formed in a horizontal and symmetrical triangular channel. Their results were compared with the previous experimental and theoretical studies and empirical equations were developed to predict the sequent depth ratio and the length of the jump and surface rollers. Ellayn, Sun [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] performed laboratory investigations to appraise the effect of a rough bed on hydraulic jump. The experiments were carried out using an artificially roughened bed with wedge-shaped baffle blocks for the Froude numbers in the range of 3.06\u0026thinsp;\u0026le;\u0026thinsp;F\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;10.95 and a relative bed roughness ranging 0.22\u0026thinsp;\u0026le;\u0026thinsp;K\u003csub\u003eR\u003c/sub\u003e\u0026le;1.4. They concluded that in the new stilling basin model, formed with the roughened bed with wedge-shaped baffle blocks, there was a reduction of 30\u0026ndash;50% in the hydraulic jump length and 16.5\u0026ndash;30% in the sequent depth compared to the smooth bed. Padulano et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] carried out experimental studies on USBSR II type to figure out its hydraulic behavior and dissipation efficiency. The effect of a continuous, transverse sill on the hydraulic jump in a rectangular channel is experimentally analyzed by Hager, Li [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. They classified submerged hydraulic jumps and hydraulic jump types from A-jump to spray. They provided the drag force and coefficients along with supposes of pressure extreme fluctuations. They also presented an assessment of dissipation efficiency for submerged and non-submerged jumps, and this assessment provided the opportunity to compare between different types of jump and classical hydraulic jump. Nandi et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] experimentally and numerically investigated the hydraulic jump that occurs in flow conditions where the Froude number varies between 2.17 and 7 with three different channel base slopes. Using the data obtained as a result of experimental modeling, they developed an empirical formula to determine the location of the hydraulic jump by regression analysis. As a result of the study, the experimental results were compared with numerical model results and it was determined that the results were quite compatible with each other. Pourabdollah et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], carried out experimentally free and submerged hydraulic jump in different stilling basins. The effects of different adverse slopes, rough beds and positive step heights on hydraulic jump characteristics in the range of 4.56\u0026thinsp;\u0026lt;\u0026thinsp;Fr\u0026thinsp;\u0026lt;\u0026thinsp;9.55 were investigated. They stated that the submerged depth ratio, lengths of the free and submerged hydraulic jumps are less than the classical hydraulic jump.\u003c/p\u003e \u003cp\u003eWhen the studies in which hydraulic jump is controlled using the sill are examined, it has been observed that studies on determining the velocity field of hydraulic jump with LDA is not enough. The LDA system has a great advantage in obtaining the velocity and turbulence characteristics of the flow without any intervention in the flow field. In addition, in the past studies, the effect of sill height on energy dissipation ratio, turbulence intensity, the length of hydraulic jump and roller was not examined in the case of the same Froude number. In addition, while the hydraulic jump occurring after the sluice gate was examined in the previous studies, in this study the hydraulic jump is evaluated in the stilling basin after the spillway chute channel ([\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. For these reasons, this study has differences from the existing literature, and it is thought to contribute to the literature.\u003c/p\u003e \u003cp\u003eIt is well known that laser Doppler Anemometry (LDA) provides quantitative information on both instantaneous and time-averaged structures of the velocity field. Using instantaneous data, detailed information on the turbulent flow field could be obtained. In the event of forced hydraulic jump, the determination of the velocity field with the LDA will contribute. In addition, turbulence intensity, hydraulic jump length and characteristics of the roller region are determined in the case of different flows and sill heights. Some experimental study is available in the literature on the hydraulic jump; however, further experimental effort is needed either to confirm the previous findings or to provide new information for different experimental and structural conditions. The aim of the present study is to determine the hydraulic jump characteristics in a stilling basin downstream of the chute channel with different slopes for the Froude numbers in the range of 7\u0026thinsp;\u0026lt;\u0026thinsp;Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;12 and relative sill heights in the range of 4\u0026thinsp;\u0026lt;\u0026thinsp;h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;13, where h\u003csub\u003es\u003c/sub\u003e is the sill height and h\u003csub\u003e1\u003c/sub\u003e is the flow depth at the toe of jump. The results from the measured velocity fields by the LDA, turbulence intensity distributions, flow profiles, energy dissipation ratios and geometrical characteristics of hydraulic jump are presented to provide a detailed evaluation of the jump in a stilling basin.\u003c/p\u003e "},{"header":"2. Experimental Setup","content":"\u003cp\u003eThe experiments were performed in a rectangular, hydraulically smooth, side surfaces and base made of glass, horizontal stilling basin downstream of a spillway chute channel shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The chute channel was 0.20 m, 0.20 m and 1.8 m wide, deep, long, respectively and the stilling basin was 0.20 m, 0.20 m and 1.50 m wide, deep, long, respectively. In the horizontal stilling basin, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, a single-row, continuous sill was installed. The slope of the downstream side of the sill was chosen as 1/2. The sill crest width (L\u003csub\u003es\u003c/sub\u003e) was determined as 2.5 cm for all sill heights. The width of the sill was the same as the width of the stilling basin. In order to control the depth of the water, a sluice gate was placed at the end of the stilling basin. The position and form of the hydraulic jump was controlled with the help of this gate. Two different spillway chute channel slopes, \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e and 12\u003csup\u003eo\u003c/sup\u003e, were used in the experiments. The velocity field was measured under three different flow conditions for each slope.\u003c/p\u003e\n\u003cp\u003eThe experiments were repeated for each sill height with different chute slopes. Experimental conditions are shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. In the table, h\u003csub\u003es\u003c/sub\u003e sill height, h\u003csub\u003e1\u003c/sub\u003e is the water depth in the pre-jump section, V\u003csub\u003e1\u003c/sub\u003e is the average flow velocity in the pre-jump section, h\u003csub\u003e2\u003c/sub\u003e is the water depth of the cross-section after the jump, L\u003csub\u003eb\u003c/sub\u003e is the length of the stilling basin, Fr\u003csub\u003e1\u003c/sub\u003e is the Froude number of the incoming flow and \u0026alpha; is slope angle of the chute channel. As can be seen from Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, when the Froude number is 12 and 10, type A and free hydraulic jump occurs, while under other flow and sill conditions, type B and submerged hydraulic jump occurs.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eExperimental conditions\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eFr\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eV\u003csub\u003e1\u003c/sub\u003e (m/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eh\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eh\u003csub\u003e2\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eL\u003csub\u003eb\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eJump Type\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"6\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e12.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e2.48\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e89\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eA/Free\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e97\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eA/Free\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e100\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eA/Free\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e10.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e1.85\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.75\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e100\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eA/Free\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.45\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e100\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eA/Free\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e100\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eA/Free\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e9.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e1.57\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.45\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e103\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e116\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e110\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"6\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e8.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9.70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e71\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e79\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e126\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e7.5\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.55\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e84\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.75\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e91\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e7.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8.25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7.70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6.70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e90\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eB/Sub.\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn the experiments, the flow velocities in the channel axis were measured with Laser Doppler Anemometer (LDA) and recorded with a Dantec LDA 62N04 flow explorer 1D high-power system, including a burst spectrum analyzer (BSA) F30 processor and integrated photo multiplier unit with BSA flow software. Laser output is supplied by operating in a wavelength of 660 nm. Beam spacing is 60 mm, and the measurable velocity fluctuation varies from 0.7 \u0026micro;m\u0026thinsp;=\u0026thinsp;s to 4.6 mm/s. The time-averaged velocity at a point was detected by postprocessing of the measured instantaneous velocities. Some turbulence characteristics of the flow can also be determined from the time series containing instantaneous velocity values. Using LDA system, the measurement time is adjusted to obtain flow parameters such as turbulence and velocity over a certain time interval or by using the number of measured data. Depending on the properties of the flow at the measurement point, the frequency, and the measured data validation levels of the LDA system can vary. Since these data are seen insufficient, the measured turbulence and velocity values were not used especially in the roller region. The LDA performs instantaneous velocity measurements with \u0026plusmn;\u0026thinsp;1% accuracy within 95% confidence interval. The postprocessing of the measured instantaneous velocities are carried out by BSA Flow software. This software includes both classic and advanced Spectrum algorithms. With the advanced Spectrum algorithm, turbulence spectra can be correctly estimated to frequencies near the mean data rate. The upper frequency limit is thus higher than that of the classic Spectrum algorithm, which shows low-pass filtering behavior, with a cut-off frequency equal to half the mean data rate. This process is done automatically by the BSA Flow software. The discharge and free surface level were measured by ultrasonic flow meter and limnimeter, respectively. As a result of the LDA measurement, the flow average velocity obtained along the depth is compared. In addition, discharge was measured with the help of a 60x60x20 chamber at the end of the channel. Thus, LDA velocity values were verified by 2 different methods.\u003c/p\u003e\n\u003cp\u003eThe relative sill height at the same Froude numbers has not clearly effect on the variation of relative length of the hydraulic jump, L\u003csub\u003ej\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e, and the relative roller zone, L\u003csub\u003er\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eThe change of h\u003csub\u003es\u003c/sub\u003e / h\u003csub\u003e1\u003c/sub\u003e ratio according to the number of Fr\u003csub\u003e1\u003c/sub\u003e is given in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. When the figure is examined, it is seen that the previous studies is not contain the cases where the h\u003csub\u003es\u003c/sub\u003e / h\u003csub\u003e1\u003c/sub\u003e ratio is greater than 8. Also, it is seen that the h\u003csub\u003es\u003c/sub\u003e / h\u003csub\u003e1\u003c/sub\u003e ratio used for 6\u0026thinsp;\u0026lt;\u0026thinsp;Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;8 in the current studies, has not been addressed in the literature.\u003c/p\u003e"},{"header":"3. Results And Discussions","content":"\u003cp\u003eThe experimental velocity profiles, free surface flow profiles, geometrical properties of hydraulic jump, turbulence intensity distributions and energy dissipation rates for different flow and sill conditions were presented. The velocities at the chute channel and the stilling basin were measured parallel to the bottom of the channel base with LDA system. The instantaneous velocities in the channel middle axis are measured and recorded with LDA and the time-averaged velocity at a point was determined by postprocessing of the measured instantaneous velocities. The Froude numbers of incoming flows for different flow and sill conditions were calculated from the velocity measurements at chute channel. The velocities at the region where air mixture is dense could not be measured with LDA.\u003c/p\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e3.1. Velocity Profiles\u003c/h2\u003e\n\u003cp\u003eThe streamwise velocity profiles at various sections of the stilling basin were presented in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e for the ranges of h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4 \u0026minus;13, chute channel slopes, \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e and \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e; Froude numbers, Fr\u0026thinsp;=\u0026thinsp;7, 7.5, 8, 9, 10, 12. The velocity profiles under the circulatory flow region are similar to those of plane turbulent wall jet. The streamwise velocities increase from zero at the stilling basin wall to a maximum value at y\u0026thinsp;=\u0026thinsp;\u0026delta;\u003csub\u003e0\u003c/sub\u003e, which is thickness of boundary layer. As can be seen from the figures, the boundary layer thickness increases with the distance from the entrance of stilling basin. The jet layer extends up to the inflexion point (change of slope of streamwise velocity, du\u003csup\u003e2\u003c/sup\u003e/dy\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0), which is the lower boundary of the roller region. A roller region that is divided by the line \u003cem\u003eu\u0026thinsp;=\u003c/em\u003e\u0026thinsp;0 into inner- and outer-regions of circulatory flow takes place above the wall-jet flow layer. Momentum exchange occurs through the null streamwise velocity line within the circulatory flow layer (Dey et al. [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. It can also be seen from the figures of the velocity profiles that the streamwise velocity, in general, tends to decrease with increasing Froude number. On the other hand, the streamwise velocity values are in a decreasing trend with increasing sill height.\u003c/p\u003e\n\u003cp\u003eThe maximum streamwise velocity occurs immediately upon entering the stilling basin for all the experiments and the intensity of the maximum streamwise velocity decreases as it moves downstream. It is clearly seen from the Figures that the peak velocity values in the stilling basin for the chute channel slopes, \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e are higher than those of the \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e. The point at which streamwise velocity attained its peak value slightly shifts to toward free surface as moving in the streamwise direction. At the same Fr numbers, the maximum streamwise velocity, in general, decreases with the increase of the sill height. The values of peak velocity decrease as the Froude number are decreased at the same height of sill for both \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e and \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e. The rate of decay of maximum wall- jet velocity for \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e is slightly greater than that for \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e. The mean rate of the decay of the maximum values is approximately 80% for all experiments.\u003c/p\u003e\n\u003cp\u003eThe thickness of the roller region increases with increasing both Froude number and sill height. The thickness of the roller zone gradually decreases as it moves downstream. The flow separation from the bed surface of the basin occurs in the just upstream of the sill. These boundary layer separations result from the increased pressure gradient and the inability of the flow to follow the geometric shape of the sill structure. The starting point of separation is located approximately at 0.5h\u003csub\u003es\u003c/sub\u003e from the sill structure and the thickness of the separation region is approximately 0.15h\u003csub\u003es\u003c/sub\u003e for all experiments. Boundary layer separation on the crest of sill and channel bottom downstream of the sill occurs for in almost all cases. In the same flow condition, the density of the air mixture in the hydraulic jump increases as the sill height decreases. In addition, the density of the air mixture increases with increasing inflow Froude number.\u003c/p\u003e\n\u003cp\u003eThe height of the side walls of the stilling basin is directly associated with the depth of water (h\u003csub\u003e2\u003c/sub\u003e) formed after hydraulic jump. The high enough side wall height prevents effective hydraulic jumping, but also plays a role in ensuring the safety of structures and riverbed in the downstream region. For \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e and 30\u003csup\u003eo\u003c/sup\u003e chute channel slopes, experimental water surface profiles obtained using limnimeter are obtained for the different Froude numbers (Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;12, 10, 9, 8, 7.5 and 7) and relative sill heights, h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e ranging from 4 to 13. The flow profiles in the jump zone were determined on average at the entrance of the stilling basin, due to the dynamic nature of the hydraulic jump and the dense air mixture.\u003c/p\u003e\n\u003cp\u003eThe figures show that with the decrease in the sill height, the amount of swelling that occurs at the upstream of the water depth and sill structure does not decrease. There is almost a uniform depth in the downstream region of the sill. Another result is that with the decrease in the Froude number, the water depth after the hydraulic jump is reduced.\u003c/p\u003e\n\u003cp\u003eFor different sill heights and Froude numbers, in different sections of the stilling basin, the ratio of the maximum horizontal velocity component obtained along the water depth to the mean flow velocity before the hydraulic jump, the change of the cross-section distance according to the depth before the hydraulic jump is given in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. It can be seen from the figure that the maximum value of u\u003csub\u003emax\u003c/sub\u003e / V\u003csub\u003e1\u003c/sub\u003e decreases with increasing sill height. For all sill heights and Froude numbers, it is determined that when the x/y\u003csub\u003e1\u003c/sub\u003e value is about 50, the jet flow loses its effect. Namely, the hydraulic jump is about to be completed. It is seen that the u\u003csub\u003emax\u003c/sub\u003e / V\u003csub\u003e1\u003c/sub\u003e value increases again in the region close to the sill for all the heights of sill and Froude numbers.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e3.2. Geometric Properties of Hydraulic Jumps\u003c/h2\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e gives the geometric properties of the hydraulic jump. The lengths of the hydraulic jump and roller zone are determined by the large amount of color experiment. In this case, the experiments of hydraulic jump recorded with high resolution camera. The lengths of hydraulic jump and roller region are determined from the videos recorded. In addition, the beginning and the end section of the hydraulic jump and roller region are controlled and verified by the measurement of the velocity profiles by using LDA. In the case of the same Froude number, L\u003csub\u003ej\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003er\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e ratios decrease with the increase of the relative sill height. In addition, as the slope of the chute channel changes from 12 \u003csup\u003eo\u003c/sup\u003e to 30 \u003csup\u003eo\u003c/sup\u003e, the L\u003csub\u003ej\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003er\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e ratios obtained for different Froude numbers are highly decreases. In cases chute channel slope is \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e, the ratio of L\u003csub\u003ej\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003er\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e generally decreases with the decrease of the Froude number, while in the case of \u0026alpha;\u0026thinsp;=\u0026thinsp;30 \u003csup\u003eo\u003c/sup\u003e, the ratios of L\u003csub\u003ej\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003er\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e increases as the Froude number increases due to the change of hydraulic jump type is from A type to B type, are given in the Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe comparison of the change of the L\u003csub\u003er\u003c/sub\u003e / h\u003csub\u003e1\u003c/sub\u003e according to the Froude number with the results of previous studies is given in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e]. While the results of this study are found to be consistent with the results of Kucukali, Chanson [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e], there is a slight difference in the results of the Froude numbers 11 and 12. The discrepancy between the present study and previous studies is thought to be due to the creation of the hydraulic jump.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e3.3 Turbulence Intensity\u003c/h2\u003e\n\u003cp\u003eThe flow has low velocity in the upstream of spillway (subcritical region) passes through the structure crest (the critical depth) and reaches high velocities on the chute channel (the super critical region). This flow, has a very high energy, is subjected to hydraulic jump to create excessive turbulence and de-energized without damaging the structure and riverbed.\u003c/p\u003e\n\u003cp\u003eThe LDA measures the instantaneous velocity values at the point where the velocity of the flow is determined and gives the opportunity to obtain the average velocity and velocity deviations related to the flow by using these values. The turbulence intensity (I) is calculated as given in Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e with the help of instantaneous point velocities in the flow region obtained by one-dimensional LDA used in the experiments:\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$$I=\\frac{{\\sqrt {\\overline {{{{u^{\\prime}}^{^{2}}}}} } }}{{\\bar {u}}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003cp\u003ewhere\u0026nbsp;\u003cimg src=\"data:image/png;base64,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\" alt=\"\" width=\"11\" height=\"18\" /\u003e\u0026nbsp;and\u0026nbsp;\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAVCAYAAAB/sn/zAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAD4SURBVDhP3Y89ioRAEIVNDExE2AsYGZjIgrmhqZ5B1kDwBoYGnsFLaCZiamYogomewh8U8e12jTOzE8wPC5vMg2pe9fu6upvDC9r3/ev9QI7j7pbv+3+YuG0b8jzHNE0UMC3LgizLyF9AVVUhyzJc16WAiR1UFIU8gfM808QgCOB5HgVMlmXBMAzyN2/UdR1xHB/d6YNJkpC/gOM4UtB13Tmgnt129Cew73tIkkSbTFEUQRCEo/sFpmkKTdNos65rhGEIURSxriuKoriCTdPQVbZtw3EcegLP8zBNE1VVXUGmtm2pzirLEsMwkL8BH+mfwJ/l83ntH9+KqtgWfhsSOgAAAABJRU5ErkJggg==\" alt=\"\" width=\"9\" height=\"19\" /\u003e\u0026nbsp;refers to the turbulence velocity deviation and\u0026nbsp;the mean velocity value at the measured point, respectively.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eFigures 12-15 show that the wall-normal profiles of streamwise turbulence intensities at the different section of the stilling basin for Froude numbers and relative sill heights used in the present study. At the entrance to the stilling basin, the streamwise turbulence intensities first increase rapidly in the near-wall region and reach at a peak value then decreases and then increases again as it moves towards the free surface. The value of maximum streamwise turbulence intensity is higher than that of the free surface in the entrance region of the basin. The peak values of the turbulence intensities take place only in the roller region of the jump as it moves towards the downstream in the hydraulic jump region. In the roller region, the maximum streamwise turbulence intensity occurs around the line u=0, where momentum exchange occurs. When the jump zone ends, the peak values of the streamwise turbulence intensity take place in the near-wall region as in the classical open channel flow. The peak values of streamwise turbulence intensity close to bottom take place in the region 0.003\u0026lt;y/d\u003csub\u003e0\u003c/sub\u003e\u0026lt;0.8, y is wall-normal ordinate and d\u003csub\u003e0\u003c/sub\u003e is vertical distance where u=u\u003csub\u003emax\u003c/sub\u003e. When the maximum values were compared, it was observed that the turbulent intensity values in the roller region were larger than those close to the bottom. It can be said from the experimental measurements that the streamwise turbulence intensity, in general, tends to increase with increasing Froude number. \u0026alpha;=12\u003csup\u003eo\u003c/sup\u003e creates larger turbulence intensities at the entrance to the stilling base compared to \u0026alpha;=30\u003csup\u003eo\u003c/sup\u003e. No clear influences of the relative sill height on the variation of the streamwise turbulence intensities.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003e3.4 Energy Dissipation Ratio in Hydraulic Jump\u003c/h2\u003e\n\u003cp\u003eThe water discharged over a spillway crest attains a very high kinetic energy and velocity at the end of spillway chute channel. This high velocity flow may cause serious scour and erosion of riverbed downstream. Hydraulic jumps are used for the reduction of energy and velocity downstream of a spillway chute. The hydraulic jump can be seen in various forms depending on the pre-jump flow conditions. The energy losses can reach up to 65\u0026ndash;85% depending on the Froude number of the incoming flow in the classical jump as in the jump occurs after the sluice gate (jump on the flat base). On the other hand, the energy losses in the hydraulic jumps occurring in the stilling basin at the downstream region of the spillway chute channel are slightly lower. The energy dissipated in the jump is represented by the loss of specific energy:\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$${E}_{L}={E}_{1}-{E}_{2}=\\left({h}_{1}+\\frac{{V}_{1}^{2}}{2g}\\right)-\\left({h}_{2}+\\frac{{V}_{2}^{2}}{2g}\\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e-a shows the energy losses in the hydraulic jump calculated using Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) for different Froude numbers of incoming flow and chute slope of \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u0026deg; and 30\u0026deg;. It is clearly seen from the figure that dissipated energy considerably increases because of the stronger jump when the Froude number is increased for both \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u0026deg; and 30\u0026deg;. The dissipation energy rate is increasing with Froude number at a faster rate for \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u0026deg; than \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u0026deg;. In Fig.\u0026nbsp;20-b, the changes of energy dissipation ratio according to h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e are presented for the chute channel slopes \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e and 12\u003csup\u003eo\u003c/sup\u003e. The dissipated energy decreases when the relative sill height, h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e, is increased for both \u0026alpha;\u0026thinsp;=\u0026thinsp;12\u0026deg; and 30\u0026deg;. Table\u0026nbsp;2 shows the ratios of dissipated energy at the hydraulic jump for different sill heights and Froude numbers. It is seen from the table that the maximum dissipated energy rate occurs for Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;12 and h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;7.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u003c/strong\u003e Energy dissipation ratios at the hydraulic jump for different structure and flow conditions\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tabn\" border=\"1\"\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u0026alpha;\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eFr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eh\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e/h\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eL\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/E\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e(%)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eFr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eh\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e/h\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eL\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/E\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003e(%)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e12.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e73\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e8.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e57\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e74\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e61\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e63\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e10.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e7.5\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e46\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e64\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e50\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e52\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e9.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003e7.0\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e36\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e51\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e40\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e48\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn addition, in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e, the changes of energy dissipation ratio according to h\u003csub\u003e1\u003c/sub\u003e/h\u003csub\u003e2\u003c/sub\u003e are presented for \u0026alpha;\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e and 12\u003csup\u003eo\u003c/sup\u003e. As can be seen from the figures, the energy losses in the hydraulic jump increase with increasing Froude number at the same ratio of h\u003csub\u003e1\u003c/sub\u003e/h\u003csub\u003e2\u003c/sub\u003e. Under conditions where the Froude number is constant, the energy loss decreases with the reduction of the h\u003csub\u003e2\u003c/sub\u003e / h\u003csub\u003e1\u003c/sub\u003e ratio.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe energy dissipation rate in the hydraulic jump in the downstream region of spillway is less than the classical hydraulic jump after the sluice gate. In the cases where the Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;12, 10 and 9, the energy dissipation rate for h\u003csub\u003es\u003c/sub\u003e= 4 cm is 72.6, 61.9 and 49.6%, the energy dissipation rate for h\u003csub\u003es\u003c/sub\u003e=3.5 cm is 74.4%, 63.5 and 51.2, respectively, for h\u003csub\u003es\u003c/sub\u003e = 3 cm this ratio is 75.7, 65.4 and 52.3%, respectively.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e18\u003c/span\u003e shows the comparison of the energy dissipation rate according to the Froude number with Fathi-Moghadam et al. [\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e]. The energy dissipation rate obtained for Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;12 is quite similar to the results obtained by Fathi-Moghadam et al. [\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e]. Besides, for Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8, there is about 10% difference in energy dissipation rate obtained with the same h\u003csub\u003es\u003c/sub\u003e / h\u003csub\u003e1\u003c/sub\u003e ratio as the results obtained by Fathi-Moghadam et al. [\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e]. Due to the submerged hydraulic jump occurring in the downstream region of the spillway, the energy dissipation rate obtained in this study is less for other flow conditions. In addition, the tail water depth influences reducing the energy dissipation rates.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusions","content":" \u003cp\u003eIn this study, experimental measurements were performed by using different Froude numbers and sill heights to determine the hydraulic jump characteristics in a stilling basin downstream of the spillway chute channel. From the measured velocity fields by LDA, the effects of Froude numbers and sill heights on hydraulic jump characteristics were investigated. The following results were found:\u003c/p\u003e \u003cp\u003eResults show that the maximum streamwise velocity occurs immediately upon entering the stilling basin for all the experiments and the intensity of the maximum streamwise velocity decreases as it moves downstream. At the same Fr numbers, the maximum streamwise velocity, in general, decreases with the increase of the sill height. The values of peak velocity decrease as the Froude number are decreased at the same height of sill for both chute channel slope α\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e and α\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e. Furthermore, the maximum value of u\u003csub\u003emax\u003c/sub\u003e / V\u003csub\u003e1\u003c/sub\u003e decreases with increasing sill height. For all sill heights and Froude numbers, it is determined that when the x/y\u003csub\u003e1\u003c/sub\u003e value is about 50, the jet flow loses its effect. Namely, the hydraulic jump is about to be completed.\u003c/p\u003e \u003cp\u003eThe relative length of the hydraulic jump and the relative roller zone increase with the decrease of the relative sill height for chute channel slope α\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e and α\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e. The experimental data show that the length of the roller region and hydraulic jump for α\u0026thinsp;=\u0026thinsp;30\u003csup\u003eo\u003c/sup\u003e are greater than those of α\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e. The thickness of the roller region increases with increasing both Froude number and sill height. The thickness of the roller zone gradually decreases as it moves downstream in the stilling basin. It can be concluded that the relative sill height at the same Froude numbers has not clearly effect on the variation of relative length of the hydraulic jump, L\u003csub\u003ej\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e, and the relative roller zone, L\u003csub\u003er\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eWhen the maximum values were compared, it was observed that the turbulent intensity values in the roller region were larger than those close to the bottom. In the roller region, the maximum streamwise turbulence intensity occurs around the line u\u0026thinsp;=\u0026thinsp;0, where momentum exchange occurs.\u003c/p\u003e \u003cp\u003eEnergy dissipation considerably increases because of the stronger jump as the Froude number is increased for both α\u0026thinsp;=\u0026thinsp;12\u0026deg; and 30\u0026deg;. The dissipated energy in the stilling basin decreases when the relative sill height is increased for both α\u0026thinsp;=\u0026thinsp;12\u0026deg; and 30\u0026deg;. In addition, the tail water depth has an effect on reducing the energy dissipation rates.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDECLARATION OF COMPETING INTEREST \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY STATEMENT\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOguz SIMSEK:\u003c/strong\u003e Conceptualization, Methodology, Validation, Formal analysis Investigation, Resources, Writing \u0026ndash; original draft, Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eM. Sami AKOZ: \u003c/strong\u003eConceptualization, Methodology, Validation, Investigation, Writing \u0026ndash; original draft, Writing \u0026ndash; review \u0026amp; editing, Supervision\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eN. Goksu SOYDAN OKSAL: \u003c/strong\u003eMethodology, Investigation, Formal analysis, Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement and Funding Information \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot Applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eChanson H (2015) Energy dissipation in hydraulic structures. CRC Press\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGumus V, Simsek O, Soydan NG, Akoz MS, Kirkgoz MS (2016) Numerical modeling of submerged hydraulic jump from a sluice gate. Journal of irrigation drainage engineering 142(1):04015037\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBakhmeteff B, Matzke A (1938) The hydraulic jump in sloped channels. Trans ASME 60 (HYD-60-l):111\u0026ndash;118\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKindsvater CE (1944) The hydraulic jump in sloping channels. Trans ASCE 109:1107\u0026ndash;1154\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBradley J, Peterka A (1957) The hydraulic design of stilling basins: hydraulic jumps on a horizontal apron (basin i). J Hydraulics Div 83(5):1\u0026ndash;24\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBunyan J (1958) SOME ASPECTS OF THE DESIGN OF HYDRAULIC STRUCTURES IN ALLUVIUM. Proceedings of the Institution of Civil Engineers 10 (2):145\u0026ndash;162\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSmith DW, Walker JH (1959) Skin-friction measurements in incompressible flow. vol\u0026nbsp;4231. National Advisory Committee for Aeronautics\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRao N, Rajaratnam N (1963) The submerged hydraulic jump. J Hydraulics Div 89(1):139\u0026ndash;162\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMahmood K (1964) Effect of apron slope on hydraulic jump performance. University of Washington\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWielogorski J, Wilson E (1970) Non-dimensional profile area coefficients for hydraulic jump in sloping rectangular channels. WATER POWER 22(4):144\u0026ndash;150, APR 1970 7 P, 13 FIG, 2 TAB, 11 REF\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHari VM (1973) Plane Jet on Sloping Floors under Finite Submergence. J Hydraulics Div 99(9):1449\u0026ndash;1460\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOhtsu I, Yasuda Y (1991) Hydraulic jump in sloping channels. J Hydraul Eng 117(7):905\u0026ndash;921\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRajaratnam N, Murahari V (1974) FLOW CHARACTERISTICS OF SLOPING CHANNEL JUMPS. J Hydraulics Div 100(HY6):731\u0026ndash;740\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMikhalev M, An HT (1976) Kinematic characteristics of a hydraulic jump on a sloping apron. Hydrotechnical Construction 10(7):686\u0026ndash;690\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHager WH (1988) B-jump in sloping channel. J Hydraul Res 26(5):539\u0026ndash;558\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSene K, Thomas N, Goldring B (1989) Planar plunge-zone flow patterns and entrained bubble transport. J Hydraul Res 27(3):363\u0026ndash;383\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKawagoshi N, Hager W (1990) B-jump in sloping channel, II. J Hydraul Res 28(4):461\u0026ndash;480\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChern M-J, Vaziri N (2020) Effect of Porous Media on Hydraulic Jump Characteristics by Using Smooth Particle Hydrodynamics Method. International Journal of Civil Engineering 18(3):367\u0026ndash;379\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKazemi F, Khodashenas SR, Sarkardeh H (2016) Experimental study of pressure fluctuation in stilling basins. International Journal of Civil Engineering 14(1):13\u0026ndash;21\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePeterka A (1958) Hydraulic design of stilling basins and energy dissipaters engineering monograph No. 25. US Bureau of Reclamation, Denver Colorado\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOhtsu I, Yasuda Y, Yamanaka Y (1991) Drag on vertical sill of forced jump. 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Journal of Zhejiang University SCIENCE A 13(7):519\u0026ndash;525\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePadulano R, Fecarotta O, Del Giudice G, Carravetta A (2017) Hydraulic design of a USBR Type II stilling basin. J Irrig Drain Eng 143(5):04017001\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNandi B, Das S, Mazumdar A, Experimental Analysis and Numerical Simulation of Hydraulic Jump. In: IOP Conference Series: Earth and Environmental Science (2020) vol\u0026nbsp;1. IOP Publishing, p\u0026nbsp;012024\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePourabdollah N, Heidarpour M, Abedi Koupai J Characteristics of free and submerged hydraulic jumps in different stilling basins. In: Proceedings of the Institution of Civil Engineers-Water Management, 2020. vol\u0026nbsp;3. 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Exp Thermal Fluid Sci 33(7):1055\u0026ndash;1064\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang H, Chanson H (2015) Experimental study of turbulent fluctuations in hydraulic jumps. J Hydraul Eng 141(7):04015010\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"LDA, Hydraulic jump, Stilling basin, Sill, Turbulence","lastPublishedDoi":"10.21203/rs.3.rs-213834/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-213834/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe hydraulic jump is a rapid transition state from supercritical to subcritical flow that occurs commonly in rivers, prismatic channels and downstream of spillways. In this study, the characteristics of the hydraulic jump in a stilling basin downstream of the spillway chute channel with the slopes of α\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e and 30\u003csup\u003eo\u003c/sup\u003e were investigated experimentally for different Froude numbers of incoming flow, Fr\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;7, 7.5, 8, 9, 10 and 12, and relative heights of sill in the range of 4\u0026thinsp;\u0026lt;\u0026thinsp;h\u003csub\u003es\u003c/sub\u003e/h\u003csub\u003e1\u003c/sub\u003e (S)\u0026thinsp;\u0026lt;\u0026thinsp;13 (S relative height). In the experiments, in which velocity field measured by laser Doppler Anemometry, it was particularly focused on the effects of both different structural configuration and flow conditions on the hydraulic jump and energy dissipation ratio. Experimental measurements showed that the length of hydraulic jump and the roller zone increases with the decrease of the sill height for α\u0026thinsp;=\u0026thinsp;12\u003csup\u003eo\u003c/sup\u003e and 30\u003csup\u003eo\u003c/sup\u003e. In addition, the length of the hydraulic jump and roller zone increased with decreasing Froude numbers. The turbulence intensity in the jump region was determined to be greater than the turbulence intensity in the region near the bottom of stilling basin. The turbulence intensity, in general, tended to decrease with decreasing Froude number.\u003c/p\u003e","manuscriptTitle":"Experimental Analysis of Hydraulic Jump at High Froude Numbers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-02-22 23:52:09","doi":"10.21203/rs.3.rs-213834/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"fcfbaf84-7248-41be-9ac6-9824dac3d16a","owner":[],"postedDate":"February 22nd, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":2566719,"name":"Civil Engineering"},{"id":2566720,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2021-07-03T14:03:45+00:00","versionOfRecord":[],"versionCreatedAt":"2021-02-22 23:52:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-213834","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-213834","identity":"rs-213834","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}