A universal law for non-breaking surface wave decay

A universal law for non-breaking surface wave decay | 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 Physical Sciences - Article A universal law for non-breaking surface wave decay Guoqiang Liu, Maryam Alshehh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9184188/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Macroscopic friction can emerge from microscopic fluctuations whose mean vanishes but whose autocorrelation does not. Here we use this statistical-mechanical route to resolve a sixty-year-old problem in ocean wave physics, how non-breaking surface waves lose energy to upper-ocean turbulence. The Navier-Stokes equations contain a stochastic vortex force (the coupling between wave orbital motion and turbulent vorticity fluctuations) that classical wave-current theory discards because its phase average is zero. Yet its finite-time autocorrelation survives, yielding a non-negative Green-Kubo transport coefficient and, with inertial-range scaling, a parameter-free decay law determined by the turbulent dissipation rate, wave frequency and gravity. Remote ocean swell, where competing processes are weak, isolates this mechanism for direct test. The same framework predicts two observational signatures that previous analyses missed. The standard satellite estimator systematically exceeds the physical decay rate because of an Ito correction, and a substantial fraction of individual tracks must display apparent energy gain. These events are not merely outliers or measurement artefacts, but the most discriminating fingerprint of the stochastic theory. Both predictions are supported by global satellite observations. Our results reveal a hidden non-breaking pathway by which upper-ocean turbulence drains wave energy into the ocean interior, and show how macroscopic dissipation can emerge from fluctuations that deterministic averaging eliminates. Earth and environmental sciences/Ocean sciences/Physical oceanography Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Statistical physics Physical sciences/Physics/Fluid dynamics Physical sciences/Physics/Applied physics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files NatureSI20260321.pdf Supplementary Information for: A universal law for non-breaking surface wave decay stochasticforcesanimation.mp4 Supplementary Video 1 Stochastic vortex force: from microscopic encounters to macroscopic friction in ocean swell decay Cite Share Download PDF Status: Under Review 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-9184188","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":615811275,"identity":"39e524ef-f192-43f9-9865-b7f6c5a5b3a6","order_by":0,"name":"Guoqiang 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survives, yielding a\r\nnon-negative Green-Kubo transport coefficient and, with\r\ninertial-range scaling, a parameter-free decay law determined by\r\nthe turbulent dissipation rate, wave frequency and gravity.\r\nRemote ocean swell, where competing processes are weak, isolates\r\nthis mechanism for direct test.\r\nThe same framework predicts two observational signatures that\r\nprevious analyses missed. The standard satellite estimator\r\nsystematically exceeds the physical decay rate because of an\r\nIto correction, and a substantial fraction of individual tracks\r\nmust display apparent energy gain.\r\nThese events are not merely outliers or measurement artefacts, but the\r\nmost discriminating fingerprint of the stochastic theory.\r\nBoth predictions are supported by global satellite observations.\r\nOur results reveal a hidden non-breaking pathway by which\r\nupper-ocean turbulence drains wave energy into the ocean interior,\r\nand show how macroscopic dissipation can emerge from fluctuations\r\nthat deterministic averaging eliminates.","manuscriptTitle":"A universal law for non-breaking surface wave decay","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-06 06:26:44","doi":"10.21203/rs.3.rs-9184188/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-physics","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"nphys","sideBox":"Learn more about [Nature Physics](http://www.nature.com/nphys/)","snPcode":"","submissionUrl":"","title":"Nature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Research","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"80acd207-301e-42cf-8107-b028510074d8","owner":[],"postedDate":"May 6th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":65529810,"name":"Earth and environmental sciences/Ocean sciences/Physical oceanography"},{"id":65529811,"name":"Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Statistical physics"},{"id":65529812,"name":"Physical sciences/Physics/Fluid dynamics"},{"id":65529813,"name":"Physical sciences/Physics/Applied physics"}],"tags":[],"updatedAt":"2026-05-06T06:26:44+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-06 06:26:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9184188","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9184188","identity":"rs-9184188","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}