Vortex rings at low Reynolds numbers in confined domains

Vortex rings at low Reynolds numbers in confined domains | 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 Vortex rings at low Reynolds numbers in confined domains Diego Silva-Soto, Martín Salinas-Vázquez, Carlos Palacios-Morales, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8329488/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a numerical investigation of vortex rings generated at low Reynolds numbers within radially confined domains. The motivation stems from the lack of previous studies addressing these combined conditions, which are relevant to wall-bounded microjet flows. We solve the governing equations using the entropy-damped artificial-compressibility (EDAC) formulation with compact finite-difference schemes (CS-FD) and a third-order total variation diminishing Runge-Kutta (TVD-RK3) method; moreover, an immersed-boundary method (IBM) resolves curvilinear walls on a Cartesian grid. Validation against high-Reynolds-number confined and low-Reynolds-number unconfined experiments, and against direct numerical simulations, confirms the solver's accuracy. We examine vortex rings with \((L/D_0=4.0)\) over \((150\leq Re\leq1000)\) and confinement ratios \((D_C/D_0=1.75,\,2.0,\,2.5)\) , plus an unconfined reference. In all cases, two dissipation zones appear: one within the ring and another near the wall. The dominant site shifts with Re : for \((Re\leq250)\) dissipation concentrates in the ring, whereas for \((Re\ge500)\) it localizes near the wall. Furthermore, confinement reduces streamwise displacement and circulation by narrowing the effective cross-section and intensifying the wall-attached vorticity layer. Decreasing Re suppresses roll-up of this layer, thereby allowing longer travel before viscous losses dominate. Lower Re also stabilizes the ring: no three-dimensionality is observed for \((Re\le 500)\) at any confinement, while at \((Re=1000)\) azimuthal undulations arise under tighter confinement ( \((D_C/D_0\le 2.0)\) ) but remain absent for \((D_C/D_0=2.5)\) , indicating that strong confinement lowers the Reynolds number threshold for breakdown. Vortex rings vortex dynamics numerical simulation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8329488","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":582110120,"identity":"643e147a-ef0e-487c-bc62-65e0d3fdcaac","order_by":0,"name":"Diego Silva-Soto","email":"","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":false,"prefix":"","firstName":"Diego","middleName":"","lastName":"Silva-Soto","suffix":""},{"id":582110121,"identity":"d65080b9-fa2a-4e61-9c3c-e4f8f36e7265","order_by":1,"name":"Martín Salinas-Vázquez","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIiWNgGAWjYHACxgMJIIq9seEA0XogWngOkqIFTEokEKlct//wgwMPd9jZG9x83Hi44JdNHoNE7sFPNxi2JTbg0GJ2I83gQOKZ5MQNtxMbDs/sSytmkMhLls5huG2MyxazGwxALW3MCZKzgVp4ew4nNkjkGIC0yOHUcv74B6CWenvJmQdBWv6DtBj/BmrhwanlQA7IlsOM/RKMDYd5fhwAaTHDb8uNnAKgluOJ/TwghzUkJ7bxvDGzzjHA45fzxzc+/NlWbc/GfvzxZ54/don97DnGt3MqbuMMMVTA2MbAwAZmGRClHgT+EK1yFIyCUTAKRhAAAP5CYNFYi4OpAAAAAElFTkSuQmCC","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":true,"prefix":"","firstName":"Martín","middleName":"","lastName":"Salinas-Vázquez","suffix":""},{"id":582110122,"identity":"eb28f870-0c29-4795-8bd1-6333775dede7","order_by":2,"name":"Carlos Palacios-Morales","email":"","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":false,"prefix":"","firstName":"Carlos","middleName":"","lastName":"Palacios-Morales","suffix":""},{"id":582110123,"identity":"73536ed6-5e8c-46be-8b30-b87345fa0af0","order_by":3,"name":"Rafael Chávez-Martínez","email":"","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":false,"prefix":"","firstName":"Rafael","middleName":"","lastName":"Chávez-Martínez","suffix":""},{"id":582110124,"identity":"4b8baea8-5ab8-4c7c-96fd-d31e90c17650","order_by":4,"name":"William Vicente","email":"","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":false,"prefix":"","firstName":"William","middleName":"","lastName":"Vicente","suffix":""}],"badges":[],"createdAt":"2025-12-10 16:23:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8329488/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8329488/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101752284,"identity":"3f916b34-69ca-4d35-aae1-a5a683a98fcc","added_by":"auto","created_at":"2026-02-03 10:26:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6024011,"visible":true,"origin":"","legend":"","description":"","filename":"ActaMechSilvaSoto.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8329488/v1_covered_4c784344-fa73-4465-8a05-da0d06903e70.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Vortex rings at low Reynolds numbers in confined domains","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Vortex rings, vortex dynamics, numerical simulation","lastPublishedDoi":"10.21203/rs.3.rs-8329488/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8329488/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a numerical investigation of vortex rings generated at low Reynolds numbers within radially confined domains. The motivation stems from the lack of previous studies addressing these combined conditions, which are relevant to wall-bounded microjet flows. We solve the governing equations using the entropy-damped artificial-compressibility (EDAC) formulation with compact finite-difference schemes (CS-FD) and a third-order total variation diminishing Runge-Kutta (TVD-RK3) method; moreover, an immersed-boundary method (IBM) resolves curvilinear walls on a Cartesian grid. Validation against high-Reynolds-number confined and low-Reynolds-number unconfined experiments, and against direct numerical simulations, confirms the solver's accuracy. We examine vortex rings with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((L/D_0=4.0)\\)\u003c/span\u003e\u003c/span\u003e over \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((150\\leq Re\\leq1000)\\)\u003c/span\u003e\u003c/span\u003e and confinement ratios \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((D_C/D_0=1.75,\\,2.0,\\,2.5)\\)\u003c/span\u003e\u003c/span\u003e, plus an unconfined reference. In all cases, two dissipation zones appear: one within the ring and another near the wall. The dominant site shifts with \u003cem\u003eRe\u003c/em\u003e: for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((Re\\leq250)\\)\u003c/span\u003e\u003c/span\u003e dissipation concentrates in the ring, whereas for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((Re\\ge500)\\)\u003c/span\u003e\u003c/span\u003e it localizes near the wall. Furthermore, confinement reduces streamwise displacement and circulation by narrowing the effective cross-section and intensifying the wall-attached vorticity layer. Decreasing \u003cem\u003eRe\u003c/em\u003e suppresses roll-up of this layer, thereby allowing longer travel before viscous losses dominate. Lower \u003cem\u003eRe\u003c/em\u003e also stabilizes the ring: no three-dimensionality is observed for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((Re\\le 500)\\)\u003c/span\u003e\u003c/span\u003e at any confinement, while at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((Re=1000)\\)\u003c/span\u003e\u003c/span\u003e azimuthal undulations arise under tighter confinement (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((D_C/D_0\\le 2.0)\\)\u003c/span\u003e\u003c/span\u003e) but remain absent for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((D_C/D_0=2.5)\\)\u003c/span\u003e\u003c/span\u003e, indicating that strong confinement lowers the Reynolds number threshold for breakdown.\u003c/p\u003e","manuscriptTitle":"Vortex rings at low Reynolds numbers in confined domains","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-30 02:43:37","doi":"10.21203/rs.3.rs-8329488/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"241bdb43-9e2b-4f74-aa19-43f2225892bb","owner":[],"postedDate":"January 30th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-13T10:56:34+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-30 02:43:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8329488","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8329488","identity":"rs-8329488","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}