Variable time step (VTS) based PTV-LIF measurements of stratified jet transitions: from plunging flows and dense bottom jets to internal hydraulic jumps

Variable time step (VTS) based PTV-LIF measurements of stratified jet transitions: from plunging flows and dense bottom jets to internal hydraulic jumps | 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 Variable time step (VTS) based PTV-LIF measurements of stratified jet transitions: from plunging flows and dense bottom jets to internal hydraulic jumps Chiun-Chau Su, Sin-Ru Liang, Hervé Capart, Steven Yueh Jen Lai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8577095/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Stratified flows driven by density differences exhibit diverse dynamic regimes, yet transitions between plunging flows, internal hydraulic jumps, and gravity plumes remain poorly characterized, particularly in confined geometries. This study addresses this gap by introducing a Variable Time Step (VTS) enhanced Particle Tracking Velocimetry-Laser Induced Fluorescence (PTV-LIF) methodology to investigate saline bottom jets in a narrow sloping channel. Isopropanol was employed as a refractive index matching agent to eliminate optical distortions, enabling simultaneous measurement of velocity and density fields using a single high-speed camera. The VTS method effectively reduced quantization errors inherent in traditional fixed-time-step algorithms, significantly improving measurement accuracy of flow and density fields. By systematically varying ambient water depths, clear transitions from plunging flows through submerged jumps and internal hydraulic jumps to gravity plumes were observed and classified for the first time. Results confirmed that flow regimes varied significantly with ambient fluid depth. Both subaerial and subaqueous hydraulic jump heights were well described by existing theoretical frameworks, though significant differences in jump lengths were observed, likely due to turbulent shear at the stratified interface. These findings extend existing regime maps and provide new experimental evidence elucidating the critical role of confinement and buoyancy in controlling stratified flow transitions, with important implications for understanding dense discharge behavior in submarine outfalls, sediment-laden river plumes, and ocean current dynamics. dense bottom jet internal hydraulic jump particle tracking velocimetry laser induced fluorescence variable time step Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 18 Mar, 2026 Reviews received at journal 17 Mar, 2026 Reviews received at journal 21 Feb, 2026 Reviewers agreed at journal 18 Feb, 2026 Reviewers agreed at journal 26 Jan, 2026 Reviewers invited by journal 23 Jan, 2026 Editor assigned by journal 15 Jan, 2026 Submission checks completed at journal 12 Jan, 2026 First submitted to journal 11 Jan, 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-8577095","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":580502177,"identity":"3d03d523-0da9-49a7-9016-b9904b2ed406","order_by":0,"name":"Chiun-Chau Su","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Chiun-Chau","middleName":"","lastName":"Su","suffix":""},{"id":580502178,"identity":"45fd0b6f-0eb6-4b18-839a-6611a1a658a5","order_by":1,"name":"Sin-Ru Liang","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Sin-Ru","middleName":"","lastName":"Liang","suffix":""},{"id":580502179,"identity":"154910c9-b0d8-4791-b4c5-3a02167bf629","order_by":2,"name":"Hervé Capart","email":"","orcid":"","institution":"National Taiwan University","correspondingAuthor":false,"prefix":"","firstName":"Hervé","middleName":"","lastName":"Capart","suffix":""},{"id":580502180,"identity":"e9fdbb28-87eb-4208-932a-bed819ab5fba","order_by":3,"name":"Steven Yueh Jen Lai","email":"data:image/png;base64,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","orcid":"","institution":"National Cheng Kung University","correspondingAuthor":true,"prefix":"","firstName":"Steven","middleName":"Yueh Jen","lastName":"Lai","suffix":""}],"badges":[],"createdAt":"2026-01-12 04:08:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8577095/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8577095/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101297620,"identity":"5f49abe4-d172-4ca0-a6f0-d1241ba5010d","added_by":"auto","created_at":"2026-01-28 09:28:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3142686,"visible":true,"origin":"","legend":"","description":"","filename":"MSdenseBottomJumpproof.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8577095/v1_covered_8970026c-20c8-4601-a79a-e965f65a3312.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Variable time step (VTS) based PTV-LIF measurements of stratified jet transitions: from plunging flows and dense bottom jets to internal hydraulic jumps","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"experiments-in-fluids","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"exif","sideBox":"Learn more about [Experiments in Fluids](http://link.springer.com/journal/348)","snPcode":"348","submissionUrl":"https://submission.nature.com/new-submission/348/3","title":"Experiments in Fluids","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"dense bottom jet, internal hydraulic jump, particle tracking velocimetry, laser induced fluorescence, variable time step","lastPublishedDoi":"10.21203/rs.3.rs-8577095/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8577095/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStratified flows driven by density differences exhibit diverse dynamic regimes, yet transitions between plunging flows, internal hydraulic jumps, and gravity plumes remain poorly characterized, particularly in confined geometries. 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