Variability of the nonlinear interaction between ultrafast Kelvin waves and the Diurnal tide over the Brazilian equatorial region

Variability of the nonlinear interaction between ultrafast Kelvin waves and the Diurnal tide over the Brazilian equatorial region | 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 Variability of the nonlinear interaction between ultrafast Kelvin waves and the Diurnal tide over the Brazilian equatorial region Fabio Egito, Moura Flavio, Ricardo Arlen Buriti, Paulo Prado Batista This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8865363/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Nonlinear interactions between atmospheric tides and planetary-scale waves play a key role in the redistribution of momentum and energy in the mesosphere and lower thermosphere (MLT). In this study, we investigate the occurrence and characteristics of nonlinear interactions between ultrafast Kelvin waves (UFKWs) and the diurnal tide over the Brazilian equatorial region, using one year of neutral wind measurements from an all-sky meteor radar at São João do Cariri (7.4°S, 36.5°W). Six UFKW events were identified through wavelet analysis. During these intervals, clear signatures of nonlinear interactions were detected, including modulation of the diurnal tide amplitude at UFKW periods and the presence of secondary waves at the sum and difference frequencies (1.25 and 0.75 cycles per day-cpd) with amplitudes of 5–15 m/s. Secondary waves also exhibited upward propagation and vertical wavelengths of 26–58 km, allowing them to reach the lower thermosphere. Comparisons between observed and theoretical vertical wavelengths revealed partial agreement with nonlinear interaction theory, indicating the importance of local atmospheric conditions. These results indicate that UFKWs play a significant role in short-term tidal variability and could contribute to vertical coupling processes in the equatorial atmosphere. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The atmosphere can support a wide range of motions across various time and spatial scales. Many of these motions are periodic and can be understood as wave phenomena. Waves play a fundamental role in atmospheric dynamics, transporting energy and momentum throughout the atmosphere. Key components of the atmospheric wave spectrum include atmospheric tides, gravity waves, and planetary-scale waves, all of which contribute to the overall wavelike motion in the atmosphere. These waves can be considered primary waves. As they propagate, they may interact with other, producing additional waves that can propagate independently through the atmosphere. This dynamic process adds further complexity to the atmospheric wave spectrum. Nonlinear interactions are characterized by the generation of secondary waves whose frequencies and wavenumbers correspond to the sum and difference of the frequencies and wavenumbers of the primary waves, as well as by the modulation of the amplitude of one primary wave at the period of the other. In the mesosphere and lower thermosphere (MLT) region, experimental evidence of nonlinear interactions between tides and planetary-scale waves have been reported since the 1980s (e.g. Manson et al., 1982 ), which reported the modulation of the semidiurnal tide at periods of approximately 5 days. Studies by Teitelbaum (1989) and Teitelbaum and Vial ( 1991 ) provided theoretical support and shed light on the observations. Since then, numerous investigations based on both observations and numerical simulations have been conducted to characterize and understand the dynamical process that take place in the nonlinear interactions between tides and planetary-scale waves (e.g. Pancheva & Mitchell., 2004; Alves et al., 2012; Huang et al., 2013 ; Nystrom et al., 2018 ; He et al., 2024 ). Nonlinear interactions participate and influence various atmospheric processes. They can induce short-term variability of tidal wave components, which could potentially affect the whole atmospheric dynamics. Nonlinear interactions also take part in atmospheric phenomena such as sudden stratospheric warmings (e.g., Chau et al., 2012; Mitra et al., 2023 ). Additionally, nonlinear interactions are one of the pathways to the coupling between the neutral and ionized atmosphere (e.g., Gan et al., 2017 ; Yamazaki et al., 2020 ; Forbes et al., 2021 ; Ma et al., 2022 ; Li et al., 2023 ). More recently, nonlinear interactions between atmospheric waves have been used to interpret a variety of periodic signals observed in atmospheric parameters (Qin et al., 2021 ; Mitra et al., 2024 ). For instance, during the 2019 minor Antarctic sudden stratospheric warming Eswaraiah et al., ( 2020 ) and Wang et al. ( 2021 ) observed a westward-propagating quasi-10-day wave (Q10DW) with zonal wavenumber one, exhibiting symmetry about the equator, which deviates from theoretical expectations. They proposed that nonlinear wave–wave interactions may have excited Q10DWs with a range of wavenumbers, potentially accounting for the observed discrepancies with the theoretical framework. Restricted to equatorial and low-latitude regions, Kelvin waves are zonally eastward-propagating waves that contribute to the planetary-scale wave spectrum. They occur in three distinct period bands: 15–20 days, 7–10 days, and 3–4 days and are referred to as slow, fast, and ultrafast Kelvin waves, respectively (Wallace and Kousky, 1968 ; Hirota, 1978 ; Salby et al., 1984 ). Ultrafast Kelvin waves (UFKWs) present longer vertical wavelengths, enabling them to propagate above the mesopause (Forbes, 2000 ). The nonlinear interaction between UFKW and atmospheric tides has been investigated through observations and numerical simulations. England et al. ( 2012 ) presented evidence of nonlinear interaction between ultrafast Kelvin waves (UFKWs) and the diurnal tide. Egito et al. ( 2018 ) also provided evidence of such interaction, including the generation of a ~ 1.3-day secondary wave, modulation of the diurnal tide amplitude, and associated variability in MLT airglow emissions. They further investigated the characteristics of the 1.3-day secondary wave and found that it propagates upward with a vertical wavelength of approximately 44 km, which is sufficiently long to penetrate into the E-region dynamo. Subsequently, Egito et al. ( 2020 ) reported a persistent 1.3-day oscillation in both ionospheric F region parameters virtual height (h'F) and the critical frequency (foF2), attributing it to modulation of the E-region dynamo wind system by the secondary wave, which highlights the role of nonlinear interactions in driving day-to-day ionospheric variability. Nystrom et al., ( 2018 ) investigated the nonlinear interactions between Kelvin waves with distinct periods and zonal wave numbers with migrating and nonmigrating diurnal tides based on numerical simulations with the thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM) from National Center for Atmospheric Research (NCAR). They found a spectrum of fifteen secondary waves generated by nonlinear interactions highlighting that nonlinear wave-wave interactions could significantly modify the way that the lower atmosphere couples with the ionosphere. Additionally, investigating the vertical structure of the secondary waves, they pointed out the discrepancy between the predicted and observed vertical structure of the secondary waves in their simulations. Understanding the occurrence of nonlinear interactions could shed light on the short-term variability of the coupled mesosphere thermosphere ionosphere system. In this study, we investigate the occurrence of nonlinear interaction between UFKW and tides, and describe the characteristics of the secondary waves generated through this interaction. Data and Analysis This study analyzes neutral wind measurements in the MLT over the Brazilian equatorial region, carried out by an all-sky meteor radar operating at São João do Cariri (7.4 o S, 36.4 o W) for the year of 2020. The radar measures neutral winds based on the reflection of Doppler-shifted echoes produced by meteor trails at altitudes between approximately 80 and 100 km. The radar transmits pulsed signals that are reflected by ionized meteor trails, which are carried by the neutral wind and are assumed to drift at the same velocity. From the Doppler-shifted echoes, it is possible to retrieve the zonal and meridional components of the neutral wind. The meteor radar at Cariri consists of one transmitting antenna and five receiving antennas. It transmits a 35.24 MHz signal with a peak power of 12 kW. Meteor echoes are grouped in altitude and time bins to infer wind components. The zonal and meridional wind components are calculated every hour at six different altitudes (82, 85, 88, 91, 94, and 98 km). To analyze the wind we applied the wavelet transform (Torrence and Compo, 1998 ); Lomb-Scargle periodogram (Lomb, 1976 ; Scargle, 1982 ) and harmonic analysis. Results UFKWs appear as transient features in the wind field, lasting only a few cycles. In contrast, tides are prominent atmospheric features that, although variable, persist in the wind field. In the equatorial MLT region, the diurnal tide is dominant. To investigate possible nonlinear interactions between UFKWs and tides, we first identified the presence of UFKWs using wavelet spectral analysis. We applied the Morlet wavelet transform (Torrence and Compo, 1998 ), which is suitable for identifying transient periodic signals, such as those left by UFKWs in the neutral wind. Figure 1 shows the wavelet power spectrum of the zonal wind (upper panel) and meridional wind (lower panel) at 91 km altitude. Black contour lines indicate regions where the signal's confidence level exceeds 90%. Horizontal dashed lines at 2.8 and 4.5 days indicate the period range associated with UFKWs. The wavelet analysis reveals several periodic variations in the zonal wind in the UFKW period range. At least six events (DOY 1–10, 60–75, 90–100, 215–230, 240–260 and 280–290) can be observed throughout the year, showing peaks in spectral energy in the zonal wind that can be associated with UFKWs. These bursts of UFKW last between 10 and 20 days, allowing them to leave its signature over at least two cycles. Wavelet spectra at other altitudes (not shown here) also exhibit a similar distribution of spectral energy associated with UFKWs. The UFKW signatures are observed during all seasons. The seasonal distribution of UFKWs described here is similar to that found in other studies (e.g., Lima et al., 2008 ). Conversely, as expected for UFKWs, no such strong signatures appear in the meridional wind, which is dominated by shorter period oscillations such as quasi-two-day oscillations. A single ground station does not provide information about the horizontal structure of the wave, but measurements of the wind at six vertical layers permit the determination of vertical profiles of amplitude and phase. From the vertical phase profile, one can infer propagation direction and vertical wavelength. To examine these features of the UFKW signatures, we performed a harmonic analysis to obtain vertical profiles of amplitude and phase. Using the least squares method, we fitted the following harmonic function to the data. \(\:y\left(t\right)={y}_{o}+Acos\left(\frac{2\pi\:\left(t-\varphi\:\right)}{T}\right)\) (1), in which y o is the mean wind, A is the wave amplitude, t is the time, T is the UFKW period and \(\:\varphi\:\) is the phase in the same units as t . We fitted Eq. (1) to the zonal wind data for the six previously listed events. Figure 2 shows the vertical profiles of amplitude and phase of UFKW signatures in the zonal wind. The colored numbers indicate the day of the year (DOY) interval. The vertical profiles show that amplitude generally increases with altitude below 91 km and decreases above this level in most cases. The largest amplitudes reach approximately 26 m/s, while the smallest are just below 10 m/s. The phase profiles exhibit downward phase propagation across all six events, indicating upward energy propagation. We determine the vertical wavelengths by analyzing the phase lag at different altitudes. This is achieved by fitting a linear function to the data, where the slope (angular coefficient) represents the vertical phase velocity. Multiplying this velocity by the wave period yields the vertical wavelength. The vertical wavelengths range from 35 to 55 km, aligning with typical values for UFKW reported in the literature (e.g., Younger and Mitchell, 2006 ; Lima et al., 2008 ). This suggests that all six cases are consistent with the presence of UFKWs in the wind field. Table 1 summarizes UFKWs features, showing maximum amplitude, vertical wavelength, observed period, and the DOY interval during which they were observed . Table 1 -Observed period, maxima amplitude and vertical wavelength of the UFKW signatures in the six events. DOY Period (days) Maxima amplitudes (m/s) \(\:{\lambda\:}_{z}\) (km) 1–10 3.9 25 36 ± 5 60–75 4.3 20 47 ± 6 90–100 3.2 17 55 ± 16 215–230 3.6 21 35 ± 2 240–260 4.2 22 43 ± 6 280–290 3.3 26 44 ± 6 In the context of the nonlinear interaction between tides and planetary-scale waves, the primary evidences of this interaction include the modulation of tidal amplitude at the periods of the planetary waves and the generation of secondary waves with frequencies equal to the sum and difference of the frequencies of the tides and planetary-scale waves. First, we analyze the variability of the diurnal tide amplitude during UFKW episodes. To extract tidal amplitudes, we applied a windowed harmonic analysis with a two day length window, forwarded by one day. This approach provides a balance between temporal resolution and stability in amplitude estimates. In the harmonic analysis, we included both the diurnal and semidiurnal tidal components, allowing us to capture the contributions of these key tidal modes and to observe how their amplitudes vary during UFKW events. By focusing on amplitude variations, this method enables us to track how UFKWs modulate tidal energy in the atmosphere, highlighting potential wave-tide interactions during active UFKW periods. Although the UFKW is prominent in the zonal wind, there are reports of secondary waves generated by nonlinear interaction between the UFKW and the diurnal tide observed in the meridional wind (England et al., 2012 ). Therefore, we also included the diurnal tide component in the meridional wind in our analysis. Figure 3 shows the amplitudes of the diurnal tide in the zonal and meridional wind across the six UFKW events, highlighting the short-term variability in diurnal tide amplitude. The diurnal tidal amplitudes consistently exhibit clear modulation at UFKW periods across most of the events in both the zonal and meridional wind. Increases and decreases in amplitude generally coincide well between these components, with a few discrepancies observed in the altitude of the modulation. During the first event (DOY 1 to 10), the amplitudes exhibit a distinct 4-day periodic variation, especially noticeable above 90 km in the zonal wind and slightly lower in the meridional wind, with pronounced peaks around DOY 3 and 7. This modulation decreases in intensity and shifts to approximately 88 km in both components. In the second event (DOY 60 to 75), two amplitude maxima appear between DOY 61 and 65 at altitudes above 90 km in both the zonal and meridional winds, resulting in a 4-day modulation. In the third event (DOY 90 to 100), the amplitude modulation is less evident; however, periodic intensifications are observed around DOY 92 and 96 at altitudes above 96 km in both components. The fourth (DOY 215–230) and fifth (DOY 240–260) events display similar characteristics, each showing three periodic intensifications, all occurring above 92 km in the zonal wind. In the meridional wind, the diurnal tide amplitudes follow a similar pattern, with enhancements occurring slightly lower in altitude. During the sixth event (DOY 280–290), the diurnal tide amplitude modulation is more prominent in the meridional wind, with enhancements observed around 90 km on days 282 and 285. In contrast, there are no traces of modulation of the diurnal tide amplitude in the zonal wind. Another evidence of the nonlinear interaction is the generation of secondary waves with frequencies equal to the sum and difference of the frequencies of the tide and the UFKW. To investigate the presence of secondary waves resulting from the nonlinear interaction between the diurnal tide and UFKW, we performed a spectral analysis using the Lomb-Scargle periodogram during the six UFKW events. Figure 4 presents the periodograms across all altitudes in the zonal and meridional wind. The three black dotted vertical lines highlight the frequencies of the two potential secondary waves (sum frequency at 1.25 cpd hereafter as SW + and difference frequency at 0.75 cpd hereafter as SW - ) as well as the UFKW reference frequency at 0.25 cpd. The diurnal tide frequency is 1 cpd. The line plots with distinct colors represent the spectrum at different altitudes. The signatures of the UFKW in the zonal wind (along with their absence and/or lower spectral energy the meridional wind) and the diurnal tide appear consistently as expected. In general, the spectral signatures of the secondary waves are somewhat irregular. Sometimes they appear as SW+, while in other cases they manifest as SW-, and their occurrence varies with altitude. In the 1st event (DOY 1–10), the SW+ appears above the confidence level from 88 to 98 km and the SW- is absent in the zonal wind. In the meridional wind, conversely, it is the SW- that appears between 88 and 98 km and there is no signature of the SW+. In the 2sd event (DOY 60–75), the signatures of the SW- show up in the zonal wind only at 94 and 98 km and there is a peak corresponding to the SW + at 82 km. In meridional wind there are no peaks at the secondary wave frequencies. In the 3rd event (DOY 90–100), there is only a signature of the SW + in the zonal wind at 82 and 85 km. In the 4th event (DOY 215–230), the signature of the SW- is observed at all altitudes in zonal and meridional wind. Although they are slightly shifted from central frequency, one should notice that the UFKW is not observed at 0.25 cycle-1 frequency and the SW frequencies are not expected to be exactly 1.25 and 0.75 cycle/day. In the 5th event (DOY 240–260), while spectral peaks associated with the SW + can be observed from 82 to 94 km at least at the significance level, there are no signatures of the SW- in the zonal wind. The meridional wind exhibits similar behavior with SW+ peaks from 85 to 91 km. In the last event (DOY 280–290), one can observe the presence of SW- signatures from 82 to 91 km and the absence of SW + in the zonal wind. In the meridional wind, it is possible to observe a similar pattern only with the additional presence of SW- signatures at 94 and 98 km. As the nonlinear interaction takes place and secondary waves are generated, they can propagate independently and produce their own effects in the atmosphere. To investigate the characteristics of these secondary waves, we performed a harmonic analysis to infer their amplitudes, propagation direction, and vertical wavelengths. We fitted Eq. (1) considering the appropriate frequency (SW + or SW-) to the cases in which the signature of a secondary wave was observed at least at three distinct altitudes. This criteria is met by the SW + and SW- observed in the first event (DOY 1–10) in the zonal and meridional wind, respectively, in the fourth event (DOY 215–230) by the SW- in both zonal and meridional wind, in the fifth (DOY 240–260) event by the SW + in the zonal and meridional wind, and in the sixth event (DOY 280–290) by the SW- in both zonal and meridional wind. Figure 5 shows the amplitudes and phases of the possible secondary waves. Black and red lines denote the zonal and meridional wind components, respectively. Typical amplitudes of the both SW + and SW- range between 5 and 15 m/s, varying with altitude and wind component. Lowest amplitudes occur below 90 km. Vertical phase profiles indicate downward phase propagation, except during the fourth event (DOY 215–230) for the SW- observed in the zonal wind. In this case, there is an inflection point in the phase profile at 91 km, with downward progression above and upward progression below. The downward phase progression in most of the cases suggests secondary waves propagate upward. The nonlinear theory predicts that the wavenumbers of the secondary waves are also the sum and difference between the wavenumbers of the primary waves, which is described in the Eq. (2) k sw = k T ± k PW (2), in which k sw , k T and k PW are the vertical wavenumbers of the secondary wave, tide and planetary wave, respectively. In terms of vertical wavelengths λ, the Eq. (2) can be expressed as follows: λ sw = λ DT λ UFK /(λ UFK ± λ DT ) (3). We evaluated whether the relationship predicted by Eq. (3) holds in the present study. The analysis utilized vertical wavelengths of the diurnal tide and the upward propagating Kelvin wave (UFKW), both derived from wind observations. The vertical wavelength of the UFKW was calculated as previously described. For the diurnal tide, we obtained the vertical wavelengths using a composite day analysis restricted to periods of UFKW activity. At each altitude level, a 24-hour composite time series was constructed by averaging wind measurements taken at the same time each day. We fitted a harmonic function as the Eq. (1) to the composite time series to derive tidal amplitudes and phases. We considered the diurnal and semidiurnal components. From these, the vertical wavelength was inferred following the same approach as for UFKW. In this context, the theoretical vertical wavelength of the secondary waves refers to that calculated from Eq. (3), while the observed wavelength corresponds to the value inferred from harmonic analysis of the secondary wave signatures in the wind field. Table 2 presents the vertical wavelengths of the diurnal tide in both the zonal and meridional wind, the UFKWs, and the theoretical and observed vertical wavelength of the secondary waves. For the fourth event (DOY 215–230), as the secondary wave observed in the zonal wind exhibited an inflection point in its phase progression at 91 km, changing from upward to downward, we do not estimate its vertical wavelength. The observed vertical wavelengths of the SW range from 26 to 58 km, whereas theoretical predictions exhibit greater variability, spanning 12 to 108 km. Overall, one can observe some discrepancy between the theoretical and observed vertical wavelengths of the SW. In the four events listed in Table 2 , a total of eight SW in the zonal and meridional wind components were identified. In the first event (DOY 1–10), both observed and theoretical vertical wavelengths of the SW- and SW + are very different. The same occurs in the fifth event (DOY 240–260), in which SW + was observed in the zonal and meridional wind. In two events (DOY 215–230 and DOY 280–290), both observed and theoretical vertical wavelengths agree with each other. In the last event (DOY 280–290), the SW- is observed in both zonal and meridional wind components, however, only the zonal wind theoretical and observed vertical wavelengths agree with each other. Table 2 Vertical wavelengths (in km) of the diurnal tide, UFKW and secondary waves in the zonal (z) and meridional (m) wind. DOY Diurnal Tide (km) UFKW (km) SW+(theo) SW+(obs) km SW-(theo) SW-(obs) 1–10 33 ± 2 (z) 27 ± 2 (m) 36 ± 5 17 ± 6 (z) 56 ± 1(z) 108 ± 17(m) 58 ± 14(m) 215–230 18 ± 3 (z) 20 ± 1 (m) 35 ± 2 37 ± 7(z) 47 ± 4(m) undefined (z) 47 ± 9 (m) 240–260 16 ± 3 (z) 24 ± 4 (m) 43 ± 6 12 ± 3 (z) 15 ± 3 (m) 26 ± 3 (z) 29 ± 3 (m) 280–290 19 ± 3 (z) 25 ± 1 (m) 44 ± 6 33 ± 7 (z) 58 ± 8 (m) 38 ± 8 (z) 32 ± 2 (m) Discussions The previous results show evidence of the nonlinear interaction between the UFKW and the diurnal tide, which include the modulation of the diurnal tide amplitudes in the zonal and meridional wind at the periods of the UFKW and presence of secondary waves. In the framework of the linear wave theory, wavelike perturbations in the atmospheric fields (e.g. wind, temperature and pressure) are supposed to be small such that the product between perturbations can be neglected. On the other hand, in the context of the nonlinear interaction, products between perturbations are not neglected and the outcome is additional wavelike solutions of the governing equations with frequencies, zonal and vertical wavenumber that are the sum and difference between the frequencies, zonal and vertical wavenumbers of the primary waves. Primary waves are expected to have significant amplitudes for nonlinear interactions to occur. Diurnal tide amplitudes in both zonal and meridional wind are systematically higher than the amplitudes of the UFKW. This might suggest that the UFKW amplitudes play an important role in the nonlinear interaction. Based on MLT meteor wind data over the equatorial region, England et al. ( 2012 ) and Egito et al. ( 2018 ) reported UFKW amplitudes of 20 m/s and almost 30 m/s, respectively, when nonlinear interaction of this wave with diurnal tide took place. In the present study, evidence of the nonlinear interaction becomes more pronounced when UFKW amplitudes reach and/or surpass 20 m/s. This occurs in most of the events, except in the 3rd event (DOY 90–100). In this event, the UFKW amplitudes stay near 10 m/s, the modulation of the diurnal tide amplitude at the UFKW period is less evident and the presence of SW signatures in the periodogram is incipient, suggesting that nonlinear interaction, if exist, is very weak. In addition to the tidal amplitude modulation, the presence of secondary waves is also indicative of the nonlinear interaction. Once they are generated, they can propagate independently and have their own effects in the atmosphere. Therefore, it is important to investigate and discuss the vertical structure of the secondary waves. The vertical phase structure of the secondary waves indicates upward propagation in almost all cases. Typical values of the observed vertical wavelengths (26 to 58 km) are large enough to enable these waves to propagate into the lower thermosphere (see Gan et al., 2017 ). Possible effects would be the modulation of the wind system of the E region dynamo, which might affect the ionosphere. The modulation of the wind system could yield the modulation of E-esporadic layers and vertical ion drifts. Egito et al. ( 2020 ) reported a 0.75 cpd (~ 1.3 day period) upward propagating secondary wave resulting from the nonlinear interaction between an UFKW and the diurnal with relatively long vertical wavelength (~ 44 km) in the MLT wind system. Corresponding modulation at the same period of the SW was observed in the h’F and foF2, indicating possible penetration into the E region dynamo with amplitude sufficiently large to transmit its effects to the F region. Future studies should address in more detail the effects of the secondary waves in the equatorial ionosphere. Testing the predictions of the nonlinear theory is important to understand its capability and limitations. In our study, the predictions of the vertical wavelengths using Eq. (3) showed partial agreement. In two cases the theoretical and observed vertical wavelengths agree with each other. The use of Eq. (3) to predict the vertical wavelengths of the secondary wave produced by nonlinear interactions between tides and planetary scale waves has shown distinct results. Based on MLT wind measurements at Esrange (68°N, 21°E), Pancheva & Mitchell ( 2004 ) observed the nonlinear between a 15 and 23-day planetary waves with the semidiurnal tide and found a good agreement between the observed and theoretical vertical wavelengths of the secondary waves produced by the nonlinear interaction. In contrast, based on numerical simulations using the NCAR TIME-GCM, Nystrom et al. ( 2018 ) did not achieve any success using Eq. (3). In their simulation, they considered the interaction between migrating and nonmigrating diurnal tides and UFKWs with zonal wavenumber 1 and 2, which resulted in a spectrum of a dozen secondary waves. To explain such a discrepant result, Nystrom et al. ( 2018 ) stated that the Eq. (2) ,that leads to Eq. (3), was assumed to be a valid input in the calculation of Teitelbaum and Vial ( 1991 ) and did not emerge as a result of the theory or the calculation. They concluded that one cannot assume a priori that wave-wave interactions lead to SW that are well expressed in terms of a single vertical wavelength, or that there is a simple relationship between the vertical wavelengths of secondary and primary waves. To understand such an argument we must look at the papers of Teitelbaum et al., ( 1989 ) and Teitelbaum and Vial ( 1991 ), which are the framework of the nonlinear interactions involving tides and planetary scale waves. Teitelbaum et al. ( 1989 ) discussed the nonlinear interaction between diurnal (DW1) and semidiurnal (SW2) migrating tides in the generation of the terdiurnal tide. In their model, they obtained the SW by solving the primitive equations, that describe the atmospheric dynamics, forced by second order nonlinear advective terms coming from the solutions of the classical linearized tidal theory, i.e., the forcing is the product of the first order solutions that describe the DW1 and SW2. The outcome was the horizontal and vertical structure of the SWs. In both first and second order solutions, they included latitude and height-dependent mean winds and temperature structures. Teitelbaum and Vial ( 1991 ), in their study of the nonlinear interaction between tides and planetary waves, adopted a simpler approach to the problem. They looked at the problem locally, i.e., assumed that nonlinear interaction between the tides and planetary waves exists. Then the relationship between wavenumbers and frequencies of the primary waves exists a priori the solution of the second order nonlinear equations, which are forced by the products of parameters of the primary waves coming from the presence of advective terms in the primitive nonlinear equations. They also do not consider mean winds. This simplifies the problem and does not capture important features of the latitudinal and vertical distributions of the SW sources. Nystrom et al. ( 2018 ) argued that advective forcing terms that drive SW and their response have very complex latitude-height distributions, and would result in multiple wave modes spanning over a range of vertical wavenumbers, which evolve with altitude due to mean wind and dissipative filtering. Therefore, the discrepancies between observed and theoretical vertical wavelengths in our study are consistent with the idea that SWs do not necessarily follow a single vertical mode, especially under realistic height-dependent conditions. Conclusions Based on a full year of meteor radar observations over the Brazilian equatorial region, six ultrafast Kelvin wave events were identified. During these intervals, the diurnal tide exhibited clear amplitude modulation at UFKW periods, and secondary waves at the predicted sum and difference frequencies were observed in both zonal and meridional winds, which indicates the occurrence of nonlinear interaction. Vertical structure of the secondary waves showed they propagate upward with vertical wavelengths ranging from 26 to 58 km. Such long vertical wavelengths enable the waves to penetrate into the lower thermosphere. Comparison between observed and theoretical vertical wavelengths revealed partial agreement, suggesting that local atmospheric conditions determine whether classical nonlinear theory can accurately describe secondary wave vertical structure. These findings reinforce the dynamical role of UFKWs in short-term tidal variability and highlight the importance of wave–wave interactions for vertical coupling in the equatorial MLT. Future work should aim to quantify the ionospheric response to these secondary waves and assess the conditions under which nonlinear predictions remain valid. Declarations Data Availability Meteor radar wind data used in this study is available upon request to the authors. Acknowledgements F. Egito and R.A. Buriti thank the Fundação de Amparo à Pesquisa do Estado da Paraíba (Fapesq) for supporting this research under the grant “Edital Universal 09/2021”. Wavelet software was provided by C. Torrence and G. Compo, and is available at URL: http://atoc.colorado.edu/research/wavelets/. Funding The present work was partially supported by the Fundação de Amparo à Pesquisa do Estado da Paraíba (Fapesq) for supporting this research under the grant “Edital Universal 09/2021” Author informations Federal University of Campina Grande, Campina Grande, Brazil F. Egito, F.P. Moura, R.A. Buriti National Institute for Space Research (INPE), São José dos Campos, Brazil. P.P. Batista Corresponding author Contact F. Egito by e-mail [email protected] Ethics declarations Ethics approval and consent to participate Not applicable. Competing interests The authors have no competing interests with any other groups. Author Contributions F. Egito conceptualized the study, performed the data analysis, and wrote the manuscript. F. Moura contributed to the data analysis and interpretation of the results. R. Buriti was responsible for the meteor radar operation, contributed to data collection, and assisted in revising the manuscript. P. P. Batista contributed to the interpretation and discussion of the results and also participated in the revision of the manuscript. References Alves EO, Lima LM, Medeiros AF, Buriti RA, Batista PP, Clemesha BR (2013) Nonlinear interaction between diurnal tidal and 2-day wave in meteor winds observed at Cachoeira Paulista-SP and São João do Cariri-PB: A case study. Revista Brasileira de Geofísica 31:403–412 Egito F, Batista IS, Takahashi H, Batista PP, Buriti RA (2020) Variability of the equatorial ionosphere induced by nonlinear interaction between an ultrafast Kelvin wave and the diurnal tide. J Atmos Solar Terr Phys 208:105397. https://doi.org/10.1016/j.jastp.2020.105397 Egito F, Buriti RA, Medeiros AF, Takahashi H (2018) Ultrafast Kelvin waves in the MLT airglow and wind, and their interaction with the atmospheric tides. Ann Geophys 36:231–241. https://doi.org/10.5194/angeo-36-231-2018 England SL, Liu G, Zhou Q, Immel TJ, Kumar KK, Ramkumar G (2012) On the signature of the quasi-3-day wave in the thermosphere during the January 2010 URSI World Day Campaign. J Geophys Research: Space Phys 117:A06304. https://doi.org/10.1029/2012JA017558 Eswaraiah S, Kim J-H, Lee W, Hwang J, Kumar KN, Kim YH (2020) Unusual changes in the Antarctic middle atmosphere during the 2019 warming in the Southern Hemisphere. Geophys Res Lett 47:e2020GL089199. https://doi.org/10.1029/2020GL089199 Forbes JM (2000) Wave coupling between the lower and upper atmosphere: Case study of an ultra-fast Kelvin wave. J Atmos Terr Phys 62:1603–1621 Forbes JM, Zhang X, Heelis R, Stoneback R, Englert CR, Harlander JM et al (2021) Atmosphere–Ionosphere coupling as viewed by ICON: Day-to-day variability due to planetary wave–tide interactions. Journal of Geophysical Research: Space Physics , 126, e2020JA028927. https://doi.org/10.1029/2020JA028927 Gan Q, Oberheide J, Yue J, Wang W (2017) Short-term variability in the ionosphere due to nonlinear interaction between the 6-day wave and migrating tides. J Geophys Research: Space Phys 122:8831–8846. https://doi.org/10.1002/2017JA023947 Gu S-Y, Teng C-K-M, Li N, Jia M, Li G, Xie H, Ding Z, Dou X (2021) Multivariate analysis on the ionospheric responses to planetary waves during the 2019 Antarctic SSW event. Journal of Geophysical Research: Space Physics , 126, e2020JA028588. https://doi.org/10.1029/2020JA028588 He M, Forbes JM, Stober G, Jacobi C, Li G, Liu L, Xu J (2024) Nonlinear interactions of planetary-scale waves in mesospheric winds observed at 52°N latitude and two longitudes. Geophys Res Lett 51:e2024GL110629. https://doi.org/10.1029/2024GL110629 Hirota I (1978) Equatorial waves in the upper stratosphere and mesosphere in relation to the semiannual oscillation of the zonal wind. J Atmos Sci 35:714–722 Huang KM, Liu AZ, Zhang SD, Yi F, Huang CM, Gan Q, Gong Y, Zhang YH (2013) A nonlinear interaction event between a 16-day wave and a diurnal tide from meteor radar observations. Ann Geophys 31:2039–2048. https://doi.org/10.5194/angeo-31-2039-2013 Li J, Tang Q, Wu Y, Zhou C, Liu Y (2023) Ionospheric 14.5-day periodic oscillation during the 2019 Antarctic SSW event. Atmosphere 14:796. https://doi.org/10.3390/atmos14050796 Lima LM, Alves EO, Medeiros AF, Buriti RA, Batista PP, Clemesha BR, Takahashi H (2008) 3–4 day Kelvin waves observed in the MLT region at 7.4°S, Brazil. Geofísica Int 47:153–160 Lomb NR (1976) Least-squares frequency analysis of unequally spaced data. Astrophys Space Sci 39:447–462 Ma Z, Gong Y, Zhang S, Xiao Q, Xue J, Huang C, Huang K (2022) Understanding the excitation of quasi-6-day waves in both hemispheres during the September 2019 Antarctic SSW. J Geophys Research: Atmos 127:e2021JD035984. https://doi.org/10.1029/2021JD035984 Manson AH, Meek CE, Gregory JB, Chakrabarty DK (1982) Fluctuations in tidal (24-, 12-h) characteristics and oscillations (8-h–5-d) in the mesosphere and lower thermosphere. Planet Space Sci 30:1283–1294. https://doi.org/10.1016/0032-0633(82)90102-7 Mitra G, Guharay A, Paulino I (2024) Signature of a zonally symmetric semidiurnal tide during major sudden stratospheric warmings and plausible mechanisms. Sci Rep 14:23806. https://doi.org/10.1038/s41598-024-72594-7 Mitra G, Guharay A, Conte JF, Chau JL (2023) Signature of two-step nonlinear interactions associated with zonally symmetric waves during major sudden stratospheric warmings. Geophys Res Lett 50:e2023GL104756. https://doi.org/10.1029/2023GL104756 Nystrom V, Gasperini F, Forbes JM, Hagan ME (2018) Exploring wave–wave interactions in a general circulation model. J Geophys Research: Space Phys 123:827–847. https://doi.org/10.1002/2017JA024984 Pancheva D, Mitchell NJ (2004) Planetary waves and variability of the semidiurnal tide in the mesosphere and lower thermosphere over Esrange (68°N, 21°E) during winter. J Phys Res 109:A08307. https://doi.org/10.1029/2004JA010433 Qin Y, Gu S-Y, Dou X (2021) A new mechanism for the generation of quasi-6-day and quasi-10-day waves during the 2019 Antarctic SSW. J Geophys Research: Atmos 126:e2021JD035568. https://doi.org/10.1029/2021JD035568 Salby ML, Hartmann DL, Bailey PL, Gille JC (1984) Evidence for equatorial Kelvin modes in Nimbus-7 LIMS. J Atmos Sci 41:220–235 Scargle JD (1982) Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astrophys J 263:835–853 Teitelbaum H, Vial F (1991) On tidal variability induced by nonlinear interaction with planetary waves. J Phys Res 96:14169–14178. https://doi.org/10.1029/91JA01019 Teitelbaum H, Vial F, Manson AH, Giraldez R, Massebeuf M (1989) Nonlinear interaction between the diurnal and semidiurnal tides: Terdiurnal and diurnal secondary waves. J Atmos Terr Phys 51:627–634 Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78 Wang JC, Palo SE, Forbes JM, Marino J, Moffat-Griffin T, Mitchell NJ (2021) Unusual quasi-10-day planetary wave activity and the ionospheric response during the 2019 Southern Hemisphere sudden stratospheric warming. Journal of Geophysical Research: Space Physics , 126, e2021JA029286. https://doi.org/10.1029/2021JA029286 Wallace JM, Kousky VE (1968) Observational evidence of Kelvin waves in the tropical stratosphere. J Atmos Sci 25:900–907 Yamazaki Y, Miyoshi Y, Xiong C, Stolle C, Soares G, Yoshikawa A (2020) Whole atmosphere model simulations of ultra-fast Kelvin wave effects in the ionosphere and thermosphere. J Geophys Research: Space Phys 125:e2020JA027939. https://doi.org/10.1029/2020JA027939 Younger PT, Mitchell NJ (2006) Waves with period near 3 days in the equatorial mesosphere and lower thermosphere over Ascension Island. J Atmos Solar Terr Phys 68:369–378 Supplementary Files figurascolunapadrao.png Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 02 Apr, 2026 Reviewers invited by journal 01 Apr, 2026 Editor assigned by journal 01 Apr, 2026 First submitted to journal 31 Mar, 2026 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. 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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-8865363","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":616215149,"identity":"d9b1bb2a-077f-4d54-ab72-d6a2dfd224ba","order_by":0,"name":"Fabio Egito","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIie2QP0vDQBTAXwjcLa90PRHtVzgQLMWQfJULgbhUEYTSsVDoFDp36HfxwoEuWlzFJe5BbuwimtcoOCRpR8H7Dce7x/3enwNwOP4gfIagKWAAXoEBZb6vskVB/aMw8CWmlDlAqWHAxGEKf8q1hSBcDub301JBnPGHZ7ATA8Nj3azgtcpXkCYLxtKXNSk4vvFWGwOjpWpUIhhLg2ASxvD8tbeF+E6g8nsLA/KxZbB+ScrnTrlF6kLKR5cidl10SIpfK1z7XqfyXu0iE1WtkhytlTirdoE821ziKGsb7MpYOw2jwdzktlTBSfVjb8V2cnE6xGalRkI8qyNBZaSms0sgol8xL/a9djgcjv/FF0bVVoPC0p/uAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-6849-9894","institution":"Universidade Federal de Campina Grande","correspondingAuthor":true,"prefix":"","firstName":"Fabio","middleName":"","lastName":"Egito","suffix":""},{"id":616215150,"identity":"0b966a07-f03a-4434-a685-e2fa1d046463","order_by":1,"name":"Moura Flavio","email":"","orcid":"","institution":"Universidade Federal de Campina Grande","correspondingAuthor":false,"prefix":"","firstName":"Moura","middleName":"","lastName":"Flavio","suffix":""},{"id":616215151,"identity":"51cbf467-5630-4021-ba7a-fa82f7e78566","order_by":2,"name":"Ricardo Arlen Buriti","email":"","orcid":"","institution":"Universidade Federal de Campina Grande","correspondingAuthor":false,"prefix":"","firstName":"Ricardo","middleName":"Arlen","lastName":"Buriti","suffix":""},{"id":616215152,"identity":"fe3f4085-3326-425e-a4b1-6757d4b3223c","order_by":3,"name":"Paulo Prado Batista","email":"","orcid":"","institution":"Instituto Nacional de Pesquisas Espaciais: Instituto Nacional de Pesquisas Espaciais","correspondingAuthor":false,"prefix":"","firstName":"Paulo","middleName":"Prado","lastName":"Batista","suffix":""}],"badges":[],"createdAt":"2026-02-12 20:09:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8865363/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8865363/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106323968,"identity":"1e42cd8a-2d67-4bbd-add7-15a32f315176","added_by":"auto","created_at":"2026-04-07 12:51:33","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":154224,"visible":true,"origin":"","legend":"\u003cp\u003eWavelet power spectrum of the zonal and meridional wind at 91 km.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/e223e69b85225ba4f0ca84a1.png"},{"id":106323967,"identity":"0d318ab3-8edd-49f4-a48c-57b63d36299b","added_by":"auto","created_at":"2026-04-07 12:51:33","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78642,"visible":true,"origin":"","legend":"\u003cp\u003eVertical structure of amplitude and phase of UFKW signatures in the zonal wind. Different colors represent different events given by DOY intervals. Phase is expressed in radians to make the comparison at distinct altitudes easier.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/eb799be85bd754b876707b79.png"},{"id":106404165,"identity":"891d5b7c-be55-40ee-9db0-d41a06e838d1","added_by":"auto","created_at":"2026-04-08 09:15:34","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":358014,"visible":true,"origin":"","legend":"\u003cp\u003eVertical profiles of amplitude of the diurnal tide in the zonal and meridional wind during the six events of UFKW. DT stands for diurnal tide.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/a084b5c3cf3292ac8c27fb83.png"},{"id":106403054,"identity":"56d54035-ee19-44d8-b909-a873da84b721","added_by":"auto","created_at":"2026-04-08 09:13:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":250576,"visible":true,"origin":"","legend":"\u003cp\u003eLomb-Scargle spectral analysis of the zonal (left) and meridional (right) wind at 82, 85, 88, 91, 94 and 98 km altitude during the six UFKW events.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/95ba5a0325b1c450743bfade.png"},{"id":106323971,"identity":"24c0956b-3497-4d12-8733-af410199c564","added_by":"auto","created_at":"2026-04-07 12:51:33","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":93924,"visible":true,"origin":"","legend":"\u003cp\u003eVertical profile of amplitude and phase of the secondary waves identified at least three distinct altitudes. Black and red lines indicate zonal and meridional wind.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/fc2d72188265c63adbb97277.png"},{"id":106405834,"identity":"7b6f339e-6a1c-413f-a448-a3f443b63ea0","added_by":"auto","created_at":"2026-04-08 09:28:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1482423,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/b56a6c9e-8a50-4b1f-80a9-c3ebb2ffec54.pdf"},{"id":106323970,"identity":"baecac31-3035-49b9-a60e-53196e179ada","added_by":"auto","created_at":"2026-04-07 12:51:33","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":781597,"visible":true,"origin":"","legend":"","description":"","filename":"figurascolunapadrao.png","url":"https://assets-eu.researchsquare.com/files/rs-8865363/v1/310c9fb1315dfe6a9ece8d78.png"}],"financialInterests":"","formattedTitle":"Variability of the nonlinear interaction between ultrafast Kelvin waves and the Diurnal tide over the Brazilian equatorial region","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe atmosphere can support a wide range of motions across various time and spatial scales. Many of these motions are periodic and can be understood as wave phenomena. Waves play a fundamental role in atmospheric dynamics, transporting energy and momentum throughout the atmosphere. Key components of the atmospheric wave spectrum include atmospheric tides, gravity waves, and planetary-scale waves, all of which contribute to the overall wavelike motion in the atmosphere. These waves can be considered primary waves. As they propagate, they may interact with other, producing additional waves that can propagate independently through the atmosphere. This dynamic process adds further complexity to the atmospheric wave spectrum.\u003c/p\u003e \u003cp\u003eNonlinear interactions are characterized by the generation of secondary waves whose frequencies and wavenumbers correspond to the sum and difference of the frequencies and wavenumbers of the primary waves, as well as by the modulation of the amplitude of one primary wave at the period of the other. In the mesosphere and lower thermosphere (MLT) region, experimental evidence of nonlinear interactions between tides and planetary-scale waves have been reported since the 1980s (e.g. Manson et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1982\u003c/span\u003e), which reported the modulation of the semidiurnal tide at periods of approximately 5 days. Studies by Teitelbaum (1989) and Teitelbaum and Vial (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) provided theoretical support and shed light on the observations. Since then, numerous investigations based on both observations and numerical simulations have been conducted to characterize and understand the dynamical process that take place in the nonlinear interactions between tides and planetary-scale waves (e.g. Pancheva \u0026amp; Mitchell., 2004; Alves et al., 2012; Huang et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Nystrom et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; He et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eNonlinear interactions participate and influence various atmospheric processes. They can induce short-term variability of tidal wave components, which could potentially affect the whole atmospheric dynamics. Nonlinear interactions also take part in atmospheric phenomena such as sudden stratospheric warmings (e.g., Chau et al., 2012; Mitra et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Additionally, nonlinear interactions are one of the pathways to the coupling between the neutral and ionized atmosphere (e.g., Gan et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Yamazaki et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Forbes et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ma et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). More recently, nonlinear interactions between atmospheric waves have been used to interpret a variety of periodic signals observed in atmospheric parameters (Qin et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Mitra et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). For instance, during the 2019 minor Antarctic sudden stratospheric warming Eswaraiah et al., (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and Wang et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) observed a westward-propagating quasi-10-day wave (Q10DW) with zonal wavenumber one, exhibiting symmetry about the equator, which deviates from theoretical expectations. They proposed that nonlinear wave\u0026ndash;wave interactions may have excited Q10DWs with a range of wavenumbers, potentially accounting for the observed discrepancies with the theoretical framework.\u003c/p\u003e \u003cp\u003eRestricted to equatorial and low-latitude regions, Kelvin waves are zonally eastward-propagating waves that contribute to the planetary-scale wave spectrum. They occur in three distinct period bands: 15\u0026ndash;20 days, 7\u0026ndash;10 days, and 3\u0026ndash;4 days and are referred to as slow, fast, and ultrafast Kelvin waves, respectively (Wallace and Kousky, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1968\u003c/span\u003e; Hirota, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1978\u003c/span\u003e; Salby et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). Ultrafast Kelvin waves (UFKWs) present longer vertical wavelengths, enabling them to propagate above the mesopause (Forbes, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). The nonlinear interaction between UFKW and atmospheric tides has been investigated through observations and numerical simulations. England et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) presented evidence of nonlinear interaction between ultrafast Kelvin waves (UFKWs) and the diurnal tide. Egito et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) also provided evidence of such interaction, including the generation of a\u0026thinsp;~\u0026thinsp;1.3-day secondary wave, modulation of the diurnal tide amplitude, and associated variability in MLT airglow emissions. They further investigated the characteristics of the 1.3-day secondary wave and found that it propagates upward with a vertical wavelength of approximately 44 km, which is sufficiently long to penetrate into the E-region dynamo. Subsequently, Egito et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) reported a persistent 1.3-day oscillation in both ionospheric F region parameters virtual height (h'F) and the critical frequency (foF2), attributing it to modulation of the E-region dynamo wind system by the secondary wave, which highlights the role of nonlinear interactions in driving day-to-day ionospheric variability. Nystrom et al., (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) investigated the nonlinear interactions between Kelvin waves with distinct periods and zonal wave numbers with migrating and nonmigrating diurnal tides based on numerical simulations with the thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM) from National Center for Atmospheric Research (NCAR). They found a spectrum of fifteen secondary waves generated by nonlinear interactions highlighting that nonlinear wave-wave interactions could significantly modify the way that the lower atmosphere couples with the ionosphere. Additionally, investigating the vertical structure of the secondary waves, they pointed out the discrepancy between the predicted and observed vertical structure of the secondary waves in their simulations.\u003c/p\u003e \u003cp\u003eUnderstanding the occurrence of nonlinear interactions could shed light on the short-term variability of the coupled mesosphere thermosphere ionosphere system. In this study, we investigate the occurrence of nonlinear interaction between UFKW and tides, and describe the characteristics of the secondary waves generated through this interaction.\u003c/p\u003e"},{"header":"Data and Analysis","content":"\u003cp\u003eThis study analyzes neutral wind measurements in the MLT over the Brazilian equatorial region, carried out by an all-sky meteor radar operating at S\u0026atilde;o Jo\u0026atilde;o do Cariri (7.4\u003csup\u003eo\u003c/sup\u003e S, 36.4\u003csup\u003eo\u003c/sup\u003e W) for the year of 2020. The radar measures neutral winds based on the reflection of Doppler-shifted echoes produced by meteor trails at altitudes between approximately 80 and 100 km. The radar transmits pulsed signals that are reflected by ionized meteor trails, which are carried by the neutral wind and are assumed to drift at the same velocity. From the Doppler-shifted echoes, it is possible to retrieve the zonal and meridional components of the neutral wind. The meteor radar at Cariri consists of one transmitting antenna and five receiving antennas. It transmits a 35.24 MHz signal with a peak power of 12 kW. Meteor echoes are grouped in altitude and time bins to infer wind components. The zonal and meridional wind components are calculated every hour at six different altitudes (82, 85, 88, 91, 94, and 98 km). To analyze the wind we applied the wavelet transform (Torrence and Compo, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1998\u003c/span\u003e); Lomb-Scargle periodogram (Lomb, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1976\u003c/span\u003e; Scargle, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1982\u003c/span\u003e) and harmonic analysis.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eUFKWs appear as transient features in the wind field, lasting only a few cycles. In contrast, tides are prominent atmospheric features that, although variable, persist in the wind field. In the equatorial MLT region, the diurnal tide is dominant. To investigate possible nonlinear interactions between UFKWs and tides, we first identified the presence of UFKWs using wavelet spectral analysis. We applied the Morlet wavelet transform (Torrence and Compo, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1998\u003c/span\u003e), which is suitable for identifying transient periodic signals, such as those left by UFKWs in the neutral wind. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the wavelet power spectrum of the zonal wind (upper panel) and meridional wind (lower panel) at 91 km altitude. Black contour lines indicate regions where the signal's confidence level exceeds 90%. Horizontal dashed lines at 2.8 and 4.5 days indicate the period range associated with UFKWs. The wavelet analysis reveals several periodic variations in the zonal wind in the UFKW period range. At least six events (DOY 1\u0026ndash;10, 60\u0026ndash;75, 90\u0026ndash;100, 215\u0026ndash;230, 240\u0026ndash;260 and 280\u0026ndash;290) can be observed throughout the year, showing peaks in spectral energy in the zonal wind that can be associated with UFKWs. These bursts of UFKW last between 10 and 20 days, allowing them to leave its signature over at least two cycles. Wavelet spectra at other altitudes (not shown here) also exhibit a similar distribution of spectral energy associated with UFKWs. The UFKW signatures are observed during all seasons. The seasonal distribution of UFKWs described here is similar to that found in other studies (e.g., Lima et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Conversely, as expected for UFKWs, no such strong signatures appear in the meridional wind, which is dominated by shorter period oscillations such as quasi-two-day oscillations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA single ground station does not provide information about the horizontal structure of the wave, but measurements of the wind at six vertical layers permit the determination of vertical profiles of amplitude and phase. From the vertical phase profile, one can infer propagation direction and vertical wavelength. To examine these features of the UFKW signatures, we performed a harmonic analysis to obtain vertical profiles of amplitude and phase. Using the least squares method, we fitted the following harmonic function to the data.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:y\\left(t\\right)={y}_{o}+Acos\\left(\\frac{2\\pi\\:\\left(t-\\varphi\\:\\right)}{T}\\right)\\)\u003c/span\u003e \u003c/span\u003e (1),\u003c/p\u003e \u003cp\u003ein which \u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e is the mean wind, \u003cem\u003eA\u003c/em\u003e is the wave amplitude, \u003cem\u003et\u003c/em\u003e is the time, T is the UFKW period and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varphi\\:\\)\u003c/span\u003e\u003c/span\u003e is the phase in the same units as \u003cem\u003et\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eWe fitted Eq.\u0026nbsp;(1) to the zonal wind data for the six previously listed events. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the vertical profiles of amplitude and phase of UFKW signatures in the zonal wind. The colored numbers indicate the day of the year (DOY) interval. The vertical profiles show that amplitude generally increases with altitude below 91 km and decreases above this level in most cases. The largest amplitudes reach approximately 26 m/s, while the smallest are just below 10 m/s. The phase profiles exhibit downward phase propagation across all six events, indicating upward energy propagation. We determine the vertical wavelengths by analyzing the phase lag at different altitudes. This is achieved by fitting a linear function to the data, where the slope (angular coefficient) represents the vertical phase velocity. Multiplying this velocity by the wave period yields the vertical wavelength. The vertical wavelengths range from 35 to 55 km, aligning with typical values for UFKW reported in the literature (e.g., Younger and Mitchell, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Lima et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). This suggests that all six cases are consistent with the presence of UFKWs in the wind field. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes UFKWs features, showing maximum amplitude, vertical wavelength, observed period, and the DOY interval during which they were observed\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e-Observed period, maxima amplitude and vertical wavelength of the UFKW signatures in the six events.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOY\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePeriod (days)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMaxima amplitudes (m/s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{z}\\)\u003c/span\u003e\u003c/span\u003e (km)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e36\u0026thinsp;\u0026plusmn;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e60\u0026ndash;75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e47\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e90\u0026ndash;100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e55\u0026thinsp;\u0026plusmn;\u0026thinsp;16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e215\u0026ndash;230\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e35\u0026thinsp;\u0026plusmn;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e240\u0026ndash;260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e43\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e280\u0026ndash;290\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e44\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the context of the nonlinear interaction between tides and planetary-scale waves, the primary evidences of this interaction include the modulation of tidal amplitude at the periods of the planetary waves and the generation of secondary waves with frequencies equal to the sum and difference of the frequencies of the tides and planetary-scale waves. First, we analyze the variability of the diurnal tide amplitude during UFKW episodes. To extract tidal amplitudes, we applied a windowed harmonic analysis with a two day length window, forwarded by one day. This approach provides a balance between temporal resolution and stability in amplitude estimates. In the harmonic analysis, we included both the diurnal and semidiurnal tidal components, allowing us to capture the contributions of these key tidal modes and to observe how their amplitudes vary during UFKW events. By focusing on amplitude variations, this method enables us to track how UFKWs modulate tidal energy in the atmosphere, highlighting potential wave-tide interactions during active UFKW periods. Although the UFKW is prominent in the zonal wind, there are reports of secondary waves generated by nonlinear interaction between the UFKW and the diurnal tide observed in the meridional wind (England et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Therefore, we also included the diurnal tide component in the meridional wind in our analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the amplitudes of the diurnal tide in the zonal and meridional wind across the six UFKW events, highlighting the short-term variability in diurnal tide amplitude. The diurnal tidal amplitudes consistently exhibit clear modulation at UFKW periods across most of the events in both the zonal and meridional wind. Increases and decreases in amplitude generally coincide well between these components, with a few discrepancies observed in the altitude of the modulation.\u003c/p\u003e \u003cp\u003eDuring the first event (DOY 1 to 10), the amplitudes exhibit a distinct 4-day periodic variation, especially noticeable above 90 km in the zonal wind and slightly lower in the meridional wind, with pronounced peaks around DOY 3 and 7. This modulation decreases in intensity and shifts to approximately 88 km in both components. In the second event (DOY 60 to 75), two amplitude maxima appear between DOY 61 and 65 at altitudes above 90 km in both the zonal and meridional winds, resulting in a 4-day modulation. In the third event (DOY 90 to 100), the amplitude modulation is less evident; however, periodic intensifications are observed around DOY 92 and 96 at altitudes above 96 km in both components. The fourth (DOY 215\u0026ndash;230) and fifth (DOY 240\u0026ndash;260) events display similar characteristics, each showing three periodic intensifications, all occurring above 92 km in the zonal wind. In the meridional wind, the diurnal tide amplitudes follow a similar pattern, with enhancements occurring slightly lower in altitude. During the sixth event (DOY 280\u0026ndash;290), the diurnal tide amplitude modulation is more prominent in the meridional wind, with enhancements observed around 90 km on days 282 and 285. In contrast, there are no traces of modulation of the diurnal tide amplitude in the zonal wind.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAnother evidence of the nonlinear interaction is the generation of secondary waves with frequencies equal to the sum and difference of the frequencies of the tide and the UFKW. To investigate the presence of secondary waves resulting from the nonlinear interaction between the diurnal tide and UFKW, we performed a spectral analysis using the Lomb-Scargle periodogram during the six UFKW events. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the periodograms across all altitudes in the zonal and meridional wind. The three black dotted vertical lines highlight the frequencies of the two potential secondary waves (sum frequency at 1.25 cpd hereafter as SW\u0026thinsp;+\u0026thinsp;and difference frequency at 0.75 cpd hereafter as SW\u003csup\u003e-\u003c/sup\u003e) as well as the UFKW reference frequency at 0.25 cpd. The diurnal tide frequency is 1 cpd. The line plots with distinct colors represent the spectrum at different altitudes. The signatures of the UFKW in the zonal wind (along with their absence and/or lower spectral energy the meridional wind) and the diurnal tide appear consistently as expected. In general, the spectral signatures of the secondary waves are somewhat irregular. Sometimes they appear as SW+, while in other cases they manifest as SW-, and their occurrence varies with altitude.\u003c/p\u003e \u003cp\u003eIn the 1st event (DOY 1\u0026ndash;10), the SW+ appears above the confidence level from 88 to 98 km and the SW- is absent in the zonal wind. In the meridional wind, conversely, it is the SW- that appears between 88 and 98 km and there is no signature of the SW+. In the 2sd event (DOY 60\u0026ndash;75), the signatures of the SW- show up in the zonal wind only at 94 and 98 km and there is a peak corresponding to the SW\u0026thinsp;+\u0026thinsp;at 82 km. In meridional wind there are no peaks at the secondary wave frequencies. In the 3rd event (DOY 90\u0026ndash;100), there is only a signature of the SW\u0026thinsp;+\u0026thinsp;in the zonal wind at 82 and 85 km. In the 4th event (DOY 215\u0026ndash;230), the signature of the SW- is observed at all altitudes in zonal and meridional wind. Although they are slightly shifted from central frequency, one should notice that the UFKW is not observed at 0.25 cycle-1 frequency and the SW frequencies are not expected to be exactly 1.25 and 0.75 cycle/day. In the 5th event (DOY 240\u0026ndash;260), while spectral peaks associated with the SW\u0026thinsp;+\u0026thinsp;can be observed from 82 to 94 km at least at the significance level, there are no signatures of the SW- in the zonal wind. The meridional wind exhibits similar behavior with SW+ peaks from 85 to 91 km. In the last event (DOY 280\u0026ndash;290), one can observe the presence of SW- signatures from 82 to 91 km and the absence of SW\u0026thinsp;+\u0026thinsp;in the zonal wind. In the meridional wind, it is possible to observe a similar pattern only with the additional presence of SW- signatures at 94 and 98 km.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the nonlinear interaction takes place and secondary waves are generated, they can propagate independently and produce their own effects in the atmosphere. To investigate the characteristics of these secondary waves, we performed a harmonic analysis to infer their amplitudes, propagation direction, and vertical wavelengths. We fitted Eq.\u0026nbsp;(1) considering the appropriate frequency (SW\u0026thinsp;+\u0026thinsp;or SW-) to the cases in which the signature of a secondary wave was observed at least at three distinct altitudes.\u003c/p\u003e \u003cp\u003eThis criteria is met by the SW\u0026thinsp;+\u0026thinsp;and SW- observed in the first event (DOY 1\u0026ndash;10) in the zonal and meridional wind, respectively, in the fourth event (DOY 215\u0026ndash;230) by the SW- in both zonal and meridional wind, in the fifth (DOY 240\u0026ndash;260) event by the SW\u0026thinsp;+\u0026thinsp;in the zonal and meridional wind, and in the sixth event (DOY 280\u0026ndash;290) by the SW- in both zonal and meridional wind. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the amplitudes and phases of the possible secondary waves. Black and red lines denote the zonal and meridional wind components, respectively. Typical amplitudes of the both SW\u0026thinsp;+\u0026thinsp;and SW- range between 5 and 15 m/s, varying with altitude and wind component. Lowest amplitudes occur below 90 km. Vertical phase profiles indicate downward phase propagation, except during the fourth event (DOY 215\u0026ndash;230) for the SW- observed in the zonal wind. In this case, there is an inflection point in the phase profile at 91 km, with downward progression above and upward progression below. The downward phase progression in most of the cases suggests secondary waves propagate upward.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe nonlinear theory predicts that the wavenumbers of the secondary waves are also the sum and difference between the wavenumbers of the primary waves, which is described in the Eq.\u0026nbsp;(2)\u003c/p\u003e \u003cp\u003e \u003cem\u003ek\u003c/em\u003e \u003csub\u003e \u003cem\u003esw\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e= k\u003c/em\u003e \u003csub\u003e \u003cem\u003eT\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e\u0026plusmn; k\u003c/em\u003e\u003csub\u003e\u003cem\u003ePW\u003c/em\u003e\u003c/sub\u003e (2),\u003c/p\u003e \u003cp\u003ein which \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003esw\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ePW\u003c/em\u003e\u003c/sub\u003e are the vertical wavenumbers of the secondary wave, tide and planetary wave, respectively.\u003c/p\u003e \u003cp\u003eIn terms of vertical wavelengths λ, the Eq.\u0026nbsp;(2) can be expressed as follows:\u003c/p\u003e \u003cp\u003eλ\u003csub\u003esw\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;λ\u003csub\u003eDT\u003c/sub\u003eλ\u003csub\u003eUFK\u003c/sub\u003e/(λ\u003csub\u003eUFK\u003c/sub\u003e\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;λ\u003csub\u003eDT\u003c/sub\u003e) (3).\u003c/p\u003e \u003cp\u003eWe evaluated whether the relationship predicted by Eq.\u0026nbsp;(3) holds in the present study. The analysis utilized vertical wavelengths of the diurnal tide and the upward propagating Kelvin wave (UFKW), both derived from wind observations. The vertical wavelength of the UFKW was calculated as previously described. For the diurnal tide, we obtained the vertical wavelengths using a composite day analysis restricted to periods of UFKW activity. At each altitude level, a 24-hour composite time series was constructed by averaging wind measurements taken at the same time each day. We fitted a harmonic function as the Eq.\u0026nbsp;(1) to the composite time series to derive tidal amplitudes and phases. We considered the diurnal and semidiurnal components. From these, the vertical wavelength was inferred following the same approach as for UFKW. In this context, the theoretical vertical wavelength of the secondary waves refers to that calculated from Eq.\u0026nbsp;(3), while the observed wavelength corresponds to the value inferred from harmonic analysis of the secondary wave signatures in the wind field. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the vertical wavelengths of the diurnal tide in both the zonal and meridional wind, the UFKWs, and the theoretical and observed vertical wavelength of the secondary waves. For the fourth event (DOY 215\u0026ndash;230), as the secondary wave observed in the zonal wind exhibited an inflection point in its phase progression at 91 km, changing from upward to downward, we do not estimate its vertical wavelength. The observed vertical wavelengths of the SW range from 26 to 58 km, whereas theoretical predictions exhibit greater variability, spanning 12 to 108 km. Overall, one can observe some discrepancy between the theoretical and observed vertical wavelengths of the SW. In the four events listed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, a total of eight SW in the zonal and meridional wind components were identified. In the first event (DOY 1\u0026ndash;10), both observed and theoretical vertical wavelengths of the SW- and SW\u0026thinsp;+\u0026thinsp;are very different. The same occurs in the fifth event (DOY 240\u0026ndash;260), in which SW\u0026thinsp;+\u0026thinsp;was observed in the zonal and meridional wind. In two events (DOY 215\u0026ndash;230 and DOY 280\u0026ndash;290), both observed and theoretical vertical wavelengths agree with each other. In the last event (DOY 280\u0026ndash;290), the SW- is observed in both zonal and meridional wind components, however, only the zonal wind theoretical and observed vertical wavelengths agree with each other.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVertical wavelengths (in km) of the diurnal tide, UFKW and secondary waves in the zonal (z) and meridional (m) wind.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOY\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDiurnal Tide (km)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUFKW\u003c/p\u003e \u003cp\u003e(km)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSW+(theo)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSW+(obs)\u003c/p\u003e \u003cp\u003ekm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSW-(theo)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSW-(obs)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33\u0026thinsp;\u0026plusmn;\u0026thinsp;2 (z)\u003c/p\u003e \u003cp\u003e27\u0026thinsp;\u0026plusmn;\u0026thinsp;2 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e36\u0026thinsp;\u0026plusmn;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e17\u0026thinsp;\u0026plusmn;\u0026thinsp;6 (z)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e56\u0026thinsp;\u0026plusmn;\u0026thinsp;1(z)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e108\u0026thinsp;\u0026plusmn;\u0026thinsp;17(m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e58\u0026thinsp;\u0026plusmn;\u0026thinsp;14(m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e215\u0026ndash;230\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (z)\u003c/p\u003e \u003cp\u003e20\u0026thinsp;\u0026plusmn;\u0026thinsp;1 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e35\u0026thinsp;\u0026plusmn;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e37\u0026thinsp;\u0026plusmn;\u0026thinsp;7(z)\u003c/p\u003e \u003cp\u003e47\u0026thinsp;\u0026plusmn;\u0026thinsp;4(m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eundefined (z)\u003c/p\u003e \u003cp\u003e47\u0026thinsp;\u0026plusmn;\u0026thinsp;9 (m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e240\u0026ndash;260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (z)\u003c/p\u003e \u003cp\u003e24\u0026thinsp;\u0026plusmn;\u0026thinsp;4 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e43\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (z)\u003c/p\u003e \u003cp\u003e15\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e26\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (z)\u003c/p\u003e \u003cp\u003e29\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e280\u0026ndash;290\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19\u0026thinsp;\u0026plusmn;\u0026thinsp;3 (z)\u003c/p\u003e \u003cp\u003e25\u0026thinsp;\u0026plusmn;\u0026thinsp;1 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e44\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e33\u0026thinsp;\u0026plusmn;\u0026thinsp;7 (z)\u003c/p\u003e \u003cp\u003e58\u0026thinsp;\u0026plusmn;\u0026thinsp;8 (m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e38\u0026thinsp;\u0026plusmn;\u0026thinsp;8 (z)\u003c/p\u003e \u003cp\u003e32\u0026thinsp;\u0026plusmn;\u0026thinsp;2 (m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Discussions","content":"\u003cp\u003eThe previous results show evidence of the nonlinear interaction between the UFKW and the diurnal tide, which include the modulation of the diurnal tide amplitudes in the zonal and meridional wind at the periods of the UFKW and presence of secondary waves. In the framework of the linear wave theory, wavelike perturbations in the atmospheric fields (e.g. wind, temperature and pressure) are supposed to be small such that the product between perturbations can be neglected. On the other hand, in the context of the nonlinear interaction, products between perturbations are not neglected and the outcome is additional wavelike solutions of the governing equations with frequencies, zonal and vertical wavenumber that are the sum and difference between the frequencies, zonal and vertical wavenumbers of the primary waves. Primary waves are expected to have significant amplitudes for nonlinear interactions to occur. Diurnal tide amplitudes in both zonal and meridional wind are systematically higher than the amplitudes of the UFKW. This might suggest that the UFKW amplitudes play an important role in the nonlinear interaction. Based on MLT meteor wind data over the equatorial region, England et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and Egito et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) reported UFKW amplitudes of 20 m/s and almost 30 m/s, respectively, when nonlinear interaction of this wave with diurnal tide took place. In the present study, evidence of the nonlinear interaction becomes more pronounced when UFKW amplitudes reach and/or surpass 20 m/s. This occurs in most of the events, except in the 3rd event (DOY 90\u0026ndash;100). In this event, the UFKW amplitudes stay near 10 m/s, the modulation of the diurnal tide amplitude at the UFKW period is less evident and the presence of SW signatures in the periodogram is incipient, suggesting that nonlinear interaction, if exist, is very weak.\u003c/p\u003e \u003cp\u003eIn addition to the tidal amplitude modulation, the presence of secondary waves is also indicative of the nonlinear interaction. Once they are generated, they can propagate independently and have their own effects in the atmosphere. Therefore, it is important to investigate and discuss the vertical structure of the secondary waves. The vertical phase structure of the secondary waves indicates upward propagation in almost all cases. Typical values of the observed vertical wavelengths (26 to 58 km) are large enough to enable these waves to propagate into the lower thermosphere (see Gan et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Possible effects would be the modulation of the wind system of the E region dynamo, which might affect the ionosphere. The modulation of the wind system could yield the modulation of E-esporadic layers and vertical ion drifts. Egito et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) reported a 0.75 cpd (~\u0026thinsp;1.3 day period) upward propagating secondary wave resulting from the nonlinear interaction between an UFKW and the diurnal with relatively long vertical wavelength (~\u0026thinsp;44 km) in the MLT wind system. Corresponding modulation at the same period of the SW was observed in the h\u0026rsquo;F and foF2, indicating possible penetration into the E region dynamo with amplitude sufficiently large to transmit its effects to the F region. Future studies should address in more detail the effects of the secondary waves in the equatorial ionosphere.\u003c/p\u003e \u003cp\u003eTesting the predictions of the nonlinear theory is important to understand its capability and limitations. In our study, the predictions of the vertical wavelengths using Eq.\u0026nbsp;(3) showed partial agreement. In two cases the theoretical and observed vertical wavelengths agree with each other. The use of Eq.\u0026nbsp;(3) to predict the vertical wavelengths of the secondary wave produced by nonlinear interactions between tides and planetary scale waves has shown distinct results. Based on MLT wind measurements at Esrange (68\u0026deg;N, 21\u0026deg;E), Pancheva \u0026amp; Mitchell (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) observed the nonlinear between a 15 and 23-day planetary waves with the semidiurnal tide and found a good agreement between the observed and theoretical vertical wavelengths of the secondary waves produced by the nonlinear interaction. In contrast, based on numerical simulations using the NCAR TIME-GCM, Nystrom et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) did not achieve any success using Eq.\u0026nbsp;(3). In their simulation, they considered the interaction between migrating and nonmigrating diurnal tides and UFKWs with zonal wavenumber 1 and 2, which resulted in a spectrum of a dozen secondary waves. To explain such a discrepant result, Nystrom et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) stated that the Eq.\u0026nbsp;(2) ,that leads to Eq.\u0026nbsp;(3), was assumed to be a valid input in the calculation of Teitelbaum and Vial (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) and did not emerge as a result of the theory or the calculation. They concluded that one cannot assume a priori that wave-wave interactions lead to SW that are well expressed in terms of a single vertical wavelength, or that there is a simple relationship between the vertical wavelengths of secondary and primary waves. To understand such an argument we must look at the papers of Teitelbaum et al., (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1989\u003c/span\u003e) and Teitelbaum and Vial (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), which are the framework of the nonlinear interactions involving tides and planetary scale waves.\u003c/p\u003e \u003cp\u003eTeitelbaum et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1989\u003c/span\u003e) discussed the nonlinear interaction between diurnal (DW1) and semidiurnal (SW2) migrating tides in the generation of the terdiurnal tide. In their model, they obtained the SW by solving the primitive equations, that describe the atmospheric dynamics, forced by second order nonlinear advective terms coming from the solutions of the classical linearized tidal theory, i.e., the forcing is the product of the first order solutions that describe the DW1 and SW2. The outcome was the horizontal and vertical structure of the SWs. In both first and second order solutions, they included latitude and height-dependent mean winds and temperature structures. Teitelbaum and Vial (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), in their study of the nonlinear interaction between tides and planetary waves, adopted a simpler approach to the problem. They looked at the problem locally, i.e., assumed that nonlinear interaction between the tides and planetary waves exists. Then the relationship between wavenumbers and frequencies of the primary waves exists a priori the solution of the second order nonlinear equations, which are forced by the products of parameters of the primary waves coming from the presence of advective terms in the primitive nonlinear equations. They also do not consider mean winds. This simplifies the problem and does not capture important features of the latitudinal and vertical distributions of the SW sources. Nystrom et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) argued that advective forcing terms that drive SW and their response have very complex latitude-height distributions, and would result in multiple wave modes spanning over a range of vertical wavenumbers, which evolve with altitude due to mean wind and dissipative filtering. Therefore, the discrepancies between observed and theoretical vertical wavelengths in our study are consistent with the idea that SWs do not necessarily follow a single vertical mode, especially under realistic height-dependent conditions.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eBased on a full year of meteor radar observations over the Brazilian equatorial region, six ultrafast Kelvin wave events were identified. During these intervals, the diurnal tide exhibited clear amplitude modulation at UFKW periods, and secondary waves at the predicted sum and difference frequencies were observed in both zonal and meridional winds, which indicates the occurrence of nonlinear interaction. Vertical structure of the secondary waves showed they propagate upward with vertical wavelengths ranging from 26 to 58 km. Such long vertical wavelengths enable the waves to penetrate into the lower thermosphere. Comparison between observed and theoretical vertical wavelengths revealed partial agreement, suggesting that local atmospheric conditions determine whether classical nonlinear theory can accurately describe secondary wave vertical structure. These findings reinforce the dynamical role of UFKWs in short-term tidal variability and highlight the importance of wave\u0026ndash;wave interactions for vertical coupling in the equatorial MLT. Future work should aim to quantify the ionospheric response to these secondary waves and assess the conditions under which nonlinear predictions remain valid.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMeteor radar wind data used in this study is available upon request to the authors.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eF. Egito and R.A. Buriti thank the Fundação de Amparo à Pesquisa do Estado da Paraíba (Fapesq) for supporting this research under the grant “Edital Universal 09/2021”. Wavelet software was provided by C. Torrence and G. Compo, and is available at URL: http://atoc.colorado.edu/research/wavelets/.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe present work was partially supported by the Fundação de Amparo à Pesquisa do Estado da Paraíba (Fapesq) for supporting this research under the grant “Edital Universal 09/2021”\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor informations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFederal University of Campina Grande, Campina Grande, Brazil\u003c/p\u003e\n\u003cp\u003eF. Egito, F.P. Moura, R.A. Buriti\u003c/p\u003e\n\u003cp\u003eNational Institute for Space Research (INPE), São José dos Campos, Brazil.\u003c/p\u003e\n\u003cp\u003eP.P. Batista\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding author\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eContact F. Egito by e-mail [email protected]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declarations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no competing interests with any other groups.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003cbr\u003e\u003c/strong\u003eF. Egito conceptualized the study, performed the data analysis, and wrote the manuscript. F. Moura contributed to the data analysis and interpretation of the results. R. Buriti was responsible for the meteor radar operation, contributed to data collection, and assisted in revising the manuscript. P. P. Batista contributed to the interpretation and discussion of the results and also participated in the revision of the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlves EO, Lima LM, Medeiros AF, Buriti RA, Batista PP, Clemesha BR (2013) Nonlinear interaction between diurnal tidal and 2-day wave in meteor winds observed at Cachoeira Paulista-SP and S\u0026atilde;o Jo\u0026atilde;o do Cariri-PB: A case study. Revista Brasileira de Geof\u0026iacute;sica 31:403\u0026ndash;412\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEgito F, Batista IS, Takahashi H, Batista PP, Buriti RA (2020) Variability of the equatorial ionosphere induced by nonlinear interaction between an ultrafast Kelvin wave and the diurnal tide. 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J Atmos Solar Terr Phys 68:369\u0026ndash;378\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8865363/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8865363/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNonlinear interactions between atmospheric tides and planetary-scale waves play a key role in the redistribution of momentum and energy in the mesosphere and lower thermosphere (MLT). In this study, we investigate the occurrence and characteristics of nonlinear interactions between ultrafast Kelvin waves (UFKWs) and the diurnal tide over the Brazilian equatorial region, using one year of neutral wind measurements from an all-sky meteor radar at S\u0026atilde;o Jo\u0026atilde;o do Cariri (7.4\u0026deg;S, 36.5\u0026deg;W). Six UFKW events were identified through wavelet analysis. During these intervals, clear signatures of nonlinear interactions were detected, including modulation of the diurnal tide amplitude at UFKW periods and the presence of secondary waves at the sum and difference frequencies (1.25 and 0.75 cycles per day-cpd) with amplitudes of 5\u0026ndash;15 m/s. Secondary waves also exhibited upward propagation and vertical wavelengths of 26\u0026ndash;58 km, allowing them to reach the lower thermosphere. Comparisons between observed and theoretical vertical wavelengths revealed partial agreement with nonlinear interaction theory, indicating the importance of local atmospheric conditions. These results indicate that UFKWs play a significant role in short-term tidal variability and could contribute to vertical coupling processes in the equatorial atmosphere.\u003c/p\u003e","manuscriptTitle":"Variability of the nonlinear interaction between ultrafast Kelvin waves and the Diurnal tide over the Brazilian equatorial region","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-07 12:51:29","doi":"10.21203/rs.3.rs-8865363/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-04-02T10:07:32+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-02T00:20:32+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-01T14:39:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth, Planets and Space","date":"2026-03-31T08:51:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f58a5b20-4cae-4253-a6db-5dcd7125aabf","owner":[],"postedDate":"April 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T12:51:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-07 12:51:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8865363","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8865363","identity":"rs-8865363","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}