Why Do Fish Swim in Circles? A Nonlinear Dynamical Perspective

Why Do Fish Swim in Circles? A Nonlinear Dynamical Perspective | 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 Short Report Why Do Fish Swim in Circles? A Nonlinear Dynamical Perspective Yifei Geng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8596342/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 The author recently visited the Monterey Bay Aquarium and observed that, in large circular tanks, the fish spontaneously swam collectively in a circular pattern. We present a minimal continuum theory that explains the spontaneous emergence of global rotational motion in confined fish schools. Starting from symmetry-based hydrodynamic equations for active matter, we show that confinement and nonlinear saturation generically give rise to a symmetry-breaking instability, driving a transition from a non-rotating disordered state to stable clockwise or counterclockwise rotating states. Our results demonstrate that rotational collective motion is a universal feature of confined active systems, provided that the fish-school density exceeds a critical threshold, and is largely independent of microscopic details. Biophysics Mathematical Physics Full Text Additional Declarations The authors declare no competing interests. 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-8596342","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":574215569,"identity":"ad104d06-cad9-42c6-ae79-c6daa5921666","order_by":0,"name":"Yifei Geng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYHCC9B8SFWAG44EHQKKBCC0PJCzOQFgHEojTwvhAorKNFC0G5xcnGNycZydnPrv5AFCLjeyGA4S03HiWkDhzW7KxzJ1jCUAtacZEaDmTcFhy24HEGRI5BkAthxOJ0HL+Y/PfOSAt+R+AWv4ToeV8QzKDZAPYFpD3DxDWInmDIY1B4liysYREGtBhBsnGMwlp4Tt/AKilxk5OQiL54YMPFXayfYS0KNxIQHEnAeUgIN9PyNBRMApGwSgYBQCbkk6Y6GfnJQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-8438-3384","institution":"Cornell University","correspondingAuthor":true,"prefix":"","firstName":"Yifei","middleName":"","lastName":"Geng","suffix":""}],"badges":[],"createdAt":"2026-01-14 01:42:36","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8596342/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8596342/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100433483,"identity":"d6a4b89b-a592-4516-b001-db67aa3b473b","added_by":"auto","created_at":"2026-01-16 15:09:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":306345,"visible":true,"origin":"","legend":"","description":"","filename":"WhyDoFishSwiminCirclesANonlinearDynamicalPerspective.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8596342/v1_covered_5dacd07f-fecb-449b-819d-1fb11e5d14db.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eWhy Do Fish Swim in Circles? 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