Measuring horizontal velocity gradients and turbulent kinetic energy at an undulating air-water interface

Measuring horizontal velocity gradients and turbulent kinetic energy at an undulating air-water interface | 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 Measuring horizontal velocity gradients and turbulent kinetic energy at an undulating air-water interface Shantanu Soumya, Nathan Laxague, Ivan Savelyev, Christopher Zappa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7410317/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Apr, 2026 Read the published version in Experiments in Fluids → Version 1 posted 11 You are reading this latest preprint version Abstract Velocity gradients are critical drivers of turbulent and scalar exchange processes within fluids. Calculating these gradients at a wavy air-water interface presents significant challenges, requiring simultaneous spatially distributed measurements of velocity fields across an undulating interface. In this study, we employ thermal marking velocimetry (TMV), an unobtrusive active velocimetry technique, to capture the surface velocity field over an unstructured grid. The surface velocity field is then used to compute the horizontal surface velocity gradient; together these enable calculation of the wave orbital velocity, surface strain, vertical vorticity, and turbulent kinetic energy (TKE). Furthermore, a structure function-based approach is employed to estimate the TKE dissipation rate at the wavy interface. Finally, we calculate the Eulerian vortex force field at the surface, providing a quantitative experimental connection between regions of surface convergence and divergence to spanwise variation in the vertical vorticity. These measurement capabilities are important for deepening our understanding of the physical processes associated with energy flux through the air-sea interface. Thermal Marking Velocimetry Surface velocity gradient Surface turbulent kinetic energy Surface kinetic energy dissipation rate Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 06 Apr, 2026 Read the published version in Experiments in Fluids → Version 1 posted Editorial decision: Revision requested 01 Oct, 2025 Reviews received at journal 01 Oct, 2025 Reviews received at journal 29 Sep, 2025 Reviewers agreed at journal 08 Sep, 2025 Reviewers agreed at journal 06 Sep, 2025 Reviewers agreed at journal 04 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers invited by journal 03 Sep, 2025 Editor assigned by journal 25 Aug, 2025 Submission checks completed at journal 20 Aug, 2025 First submitted to journal 19 Aug, 2025 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. 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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-7410317","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511790149,"identity":"92eb41bc-c617-4508-8216-48f111d35d73","order_by":0,"name":"Shantanu Soumya","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYBAC+RkwFv8BMCXHwMADpNhwazG4ASTAiiUSwALGhLVIwLVABBIbCGqRbn72+EPNncQGCeZjUjfb7NI33O49wPCh7DBuv8w5Zm5w4NizxAb+Y2nSuW3JuRvunEtgnHEOtxaGGwlmEgfYDgPdk2MG1MKcu+FGjgEzbxs+LenfJA78g2upTzcAafmLV0uOmcTBNriWwwlgLYx4tAAVlEmc7Tts3CaRlmydc+644UygloM959Jxe39G+jaJim+HZfv5Dx+8nVNWLc93I8fwwY8ya9wOgwFwRDBCo+MAYfVw8IcEtaNgFIyCUTBiAABcKVx/tZtCMQAAAABJRU5ErkJggg==","orcid":"","institution":"University of New Hampshire","correspondingAuthor":true,"prefix":"","firstName":"Shantanu","middleName":"","lastName":"Soumya","suffix":""},{"id":511790150,"identity":"021549b3-17d8-433d-992d-c0ec3a893574","order_by":1,"name":"Nathan Laxague","email":"","orcid":"","institution":"University of New Hampshire","correspondingAuthor":false,"prefix":"","firstName":"Nathan","middleName":"","lastName":"Laxague","suffix":""},{"id":511790152,"identity":"cb5c27c4-7f96-4f3d-a34d-229fca01a878","order_by":2,"name":"Ivan Savelyev","email":"","orcid":"","institution":"United States Naval Research Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Ivan","middleName":"","lastName":"Savelyev","suffix":""},{"id":511790153,"identity":"74d8d7d7-3fff-4ea3-a07b-80d1ffb80f15","order_by":3,"name":"Christopher Zappa","email":"","orcid":"","institution":"Columbia University","correspondingAuthor":false,"prefix":"","firstName":"Christopher","middleName":"","lastName":"Zappa","suffix":""}],"badges":[],"createdAt":"2025-08-19 15:53:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7410317/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7410317/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00348-026-04195-1","type":"published","date":"2026-04-06T15:56:59+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":106808740,"identity":"73e5710a-cad6-4b6a-a53c-3a2f1281fa68","added_by":"auto","created_at":"2026-04-13 15:59:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4151380,"visible":true,"origin":"","legend":"","description":"","filename":"Soumya2023TMVExpFluids.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7410317/v1_covered_64c97f5b-5451-41bc-beaf-28aa8c5d9d8a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Measuring horizontal velocity gradients and turbulent kinetic energy at an undulating air-water interface","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Thermal Marking Velocimetry, Surface velocity gradient, Surface turbulent kinetic energy, Surface kinetic energy dissipation rate","lastPublishedDoi":"10.21203/rs.3.rs-7410317/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7410317/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Velocity gradients are critical drivers of turbulent and scalar exchange processes within fluids. 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