Eulerian and Lagrangian characterization of a high-amplitude convectively unstable shoaling internal solitary wave in two dimensions.

Eulerian and Lagrangian characterization of a high-amplitude convectively unstable shoaling internal solitary wave in two dimensions. | 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 Eulerian and Lagrangian characterization of a high-amplitude convectively unstable shoaling internal solitary wave in two dimensions. Tilemachos Bolioudakis, Greg N. Thomsen, Peter J. Diamessis, Ren-Chieh Lien, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7906656/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Apr, 2026 Read the published version in Ocean Dynamics → Version 1 posted 10 You are reading this latest preprint version Abstract High-amplitude Internal Solitary Waves (ISWs), shoaling over a realistic transect of the gentle bathymetric slope in the South China Sea, are subject to subsurface convective instability (Umax > C), which, in conjunction with the near-surface shear structure of the baroclinic background current, supports the development of a subsurface recirculating core. Through this core and its dynamic evolution, ISWs act as key drivers of material and mass transport. Via the one-way online coupling of a high-resolution, fully nonlinear non-hydrostatic flow solver integrated with a high-accuracy particle-tracking scheme, two-dimensional simulations of a single propagating ISW are conducted. The interaction between the formation and dynamic evolution of the ISW’s convectively-driven recirculating core, its associated vortical structures, and the trajectories of neutrally buoyant particles are examined. Particular emphasis is placed on identifying the primary entrainment pathway along a negative-vorticity layer at the rear of the ISW, as well as secondary entrainment routes subsequently emerging from the top and bottom of the core. In contrast, detrainment is found to occur primarily through a narrow channel in the ISW rear. These features are corroborated by Finite-Time Lyapunov Exponent (FTLE) analysis. The size and shape of the recirculating core are further examined using Lagrangian Coherent Structures (LCS), providing a complementary perspective to the classical Eulerian criterion based on Umax > C. Finally, long-range particle transport and residence times are quantified, reaching O(10 km) and durations on the order of hours, respectively, for a substantial fraction of entrained particles. Internal Solitary Waves Subsurface Core Lagrangian Transport Particle Tracking Numerical Simulation Full Text Additional Declarations No competing interests reported. Supplementary Files ReadmeSupplementaryAnimationOcDynBolioudakis.pdf OcDynSupplementaryAnimationBolioudakisetal.mp4 Cite Share Download PDF Status: Published Journal Publication published 29 Apr, 2026 Read the published version in Ocean Dynamics → Version 1 posted Editorial decision: Accepted 08 Apr, 2026 Reviews received at journal 07 Apr, 2026 Reviews received at journal 26 Mar, 2026 Reviewers agreed at journal 11 Mar, 2026 Reviewers agreed at journal 06 Mar, 2026 Reviewers agreed at journal 12 Nov, 2025 Reviewers invited by journal 31 Oct, 2025 Editor assigned by journal 20 Oct, 2025 Submission checks completed at journal 20 Oct, 2025 First submitted to journal 20 Oct, 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7906656","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":544235314,"identity":"0068a97a-76d2-4a02-ad79-88cb8a983a96","order_by":0,"name":"Tilemachos Bolioudakis","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIiWNgGAWjYDACCYbEBxIVYCbjgQdAooGQDh4JhscGFmcgnAMJxGlhfCZR2UaKFnvp5gSJm/Ps5MxnNx8AarGR3XCAkC0yxxIMZ25LNpa5cywBqCXNmLAWiZyEZMltBxJnSOQYALUcTiRCS/6Hw3/ngLTkfwBq+U+MloTEBskGsC0g7x8gQsudA8kMEseSjSUk0oAOM0g2nklIC/vshvQfEjV2chISyQ8ffKiwk+0jpAUNGJCmfBSMglEwCkYBDgAAP4dINEN/dkwAAAAASUVORK5CYII=","orcid":"","institution":"Cornell University","correspondingAuthor":true,"prefix":"","firstName":"Tilemachos","middleName":"","lastName":"Bolioudakis","suffix":""},{"id":544235315,"identity":"3fc2110c-057d-4724-a5f1-8f5aa97b87e4","order_by":1,"name":"Greg N. Thomsen","email":"","orcid":"","institution":"Wandering Wakhs Research","correspondingAuthor":false,"prefix":"","firstName":"Greg","middleName":"N.","lastName":"Thomsen","suffix":""},{"id":544235316,"identity":"366650e9-771f-4b2e-9477-8d62fbc445ab","order_by":2,"name":"Peter J. Diamessis","email":"","orcid":"","institution":"Cornell University","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"J.","lastName":"Diamessis","suffix":""},{"id":544235317,"identity":"62b9ea4b-287e-4de5-bd7c-f934b8c302c0","order_by":3,"name":"Ren-Chieh Lien","email":"","orcid":"","institution":"University of Washington","correspondingAuthor":false,"prefix":"","firstName":"Ren-Chieh","middleName":"","lastName":"Lien","suffix":""},{"id":544235318,"identity":"1e409f7f-7f14-4f8a-a2a2-9e27febc493a","order_by":4,"name":"Kevin G. Lamb","email":"","orcid":"","institution":"University of Waterloo","correspondingAuthor":false,"prefix":"","firstName":"Kevin","middleName":"G.","lastName":"Lamb","suffix":""},{"id":544235319,"identity":"1ef0cad8-a4fc-4dd2-a4b5-af7581c664ca","order_by":5,"name":"John Winnicki","email":"","orcid":"","institution":"Stanford University","correspondingAuthor":false,"prefix":"","firstName":"John","middleName":"","lastName":"Winnicki","suffix":""},{"id":544235320,"identity":"f4fa9fb8-c353-4b71-8c6c-a5ac0f079cc7","order_by":6,"name":"Gustaaf Jacobs","email":"","orcid":"","institution":"San Diego State University","correspondingAuthor":false,"prefix":"","firstName":"Gustaaf","middleName":"","lastName":"Jacobs","suffix":""}],"badges":[],"createdAt":"2025-10-20 14:23:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7906656/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7906656/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10236-026-01805-8","type":"published","date":"2026-04-29T15:58:03+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95911347,"identity":"4fc494c9-9f45-454e-b48f-e6b500a4eb12","added_by":"auto","created_at":"2025-11-14 10:31:56","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9294,"visible":true,"origin":"","legend":"","description":"","filename":"6326c9f78b884d2bbdb1b034a3856607.json","url":"https://assets-eu.researchsquare.com/files/rs-7906656/v1/8364081c6865e37a061ca575.json"},{"id":108437690,"identity":"5c94f56e-d41b-429f-9ca6-5cf9ca54fc9c","added_by":"auto","created_at":"2026-05-04 16:02:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2141704,"visible":true,"origin":"","legend":"","description":"","filename":"Bolioudakisetal2025OcDynLaTexCodes.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7906656/v1_covered_7062084d-6e87-44bd-948c-81963e969452.pdf"},{"id":95911346,"identity":"25b72c57-46c3-4212-9bc6-36354fae94bb","added_by":"auto","created_at":"2025-11-14 10:31:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":68469,"visible":true,"origin":"","legend":"","description":"","filename":"ReadmeSupplementaryAnimationOcDynBolioudakis.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7906656/v1/4d5965a52f5e7ac91f4ebc00.pdf"},{"id":95911369,"identity":"14a8487f-3834-43e1-adce-29c0505195fb","added_by":"auto","created_at":"2025-11-14 10:31:57","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":18483137,"visible":true,"origin":"","legend":"","description":"","filename":"OcDynSupplementaryAnimationBolioudakisetal.mp4","url":"https://assets-eu.researchsquare.com/files/rs-7906656/v1/5889b273a40d6e3d953c2c27.mp4"}],"financialInterests":"No competing interests reported.","formattedTitle":"Eulerian and Lagrangian characterization of a high-amplitude convectively unstable shoaling internal solitary wave in two dimensions.","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":"ocean-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"odyn","sideBox":"Learn more about [Ocean Dynamics](https://link.springer.com/journal/10236)","snPcode":"10236","submissionUrl":"https://submission.springernature.com/new-submission/10236/3","title":"Ocean Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Internal Solitary Waves, Subsurface Core, Lagrangian Transport, Particle Tracking, Numerical Simulation","lastPublishedDoi":"10.21203/rs.3.rs-7906656/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7906656/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"High-amplitude Internal Solitary Waves (ISWs), shoaling over a realistic transect of the gentle bathymetric slope in the South China Sea, are subject to subsurface convective instability (Umax \u003e C), which, in conjunction with the near-surface shear structure of the baroclinic background current, supports the development of a subsurface recirculating core. Through this core and its dynamic evolution, ISWs act as key drivers of material and mass transport. Via the one-way online coupling of a high-resolution, fully nonlinear non-hydrostatic flow solver integrated with a high-accuracy particle-tracking scheme, two-dimensional simulations of a single propagating ISW are conducted. The interaction between the formation and dynamic evolution of the ISW’s convectively-driven recirculating core, its associated vortical structures, and the trajectories of neutrally buoyant particles are examined. Particular emphasis is placed on identifying the primary entrainment pathway along a negative-vorticity layer at the rear of the ISW, as well as secondary entrainment routes subsequently emerging from the top and bottom of the core. In contrast, detrainment is found to occur primarily through a narrow channel in the ISW rear. These features are corroborated by Finite-Time Lyapunov Exponent (FTLE) analysis. The size and shape of the recirculating core are further examined using Lagrangian Coherent Structures (LCS), providing a complementary perspective to the classical Eulerian criterion based on Umax \u003e C. Finally, long-range particle transport and residence times are quantified, reaching O(10 km) and durations on the order of hours, respectively, for a substantial fraction of entrained particles.","manuscriptTitle":"Eulerian and Lagrangian characterization of a high-amplitude convectively unstable shoaling internal solitary wave in two dimensions.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-14 10:31:50","doi":"10.21203/rs.3.rs-7906656/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2026-04-08T11:32:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-08T00:51:05+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-26T13:24:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"204467555170562267157764310747981872964","date":"2026-03-11T06:08:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"130186923428956279603751181606335926712","date":"2026-03-06T09:38:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"335579940086020124121327193007130506919","date":"2025-11-13T02:41:08+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-31T22:08:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-21T01:58:46+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-21T01:57:43+00:00","index":"","fulltext":""},{"type":"submitted","content":"Ocean Dynamics","date":"2025-10-20T14:18:55+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"ocean-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"odyn","sideBox":"Learn more about [Ocean Dynamics](https://link.springer.com/journal/10236)","snPcode":"10236","submissionUrl":"https://submission.springernature.com/new-submission/10236/3","title":"Ocean Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"391f5fcc-6e20-47b1-be9c-3810b011f86c","owner":[],"postedDate":"November 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-05-04T16:01:02+00:00","versionOfRecord":{"articleIdentity":"rs-7906656","link":"https://doi.org/10.1007/s10236-026-01805-8","journal":{"identity":"ocean-dynamics","isVorOnly":false,"title":"Ocean Dynamics"},"publishedOn":"2026-04-29 15:58:03","publishedOnDateReadable":"April 29th, 2026"},"versionCreatedAt":"2025-11-14 10:31:50","video":"","vorDoi":"10.1007/s10236-026-01805-8","vorDoiUrl":"https://doi.org/10.1007/s10236-026-01805-8","workflowStages":[]},"version":"v1","identity":"rs-7906656","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7906656","identity":"rs-7906656","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}