Tracking the nonlinear formation of an interfacial wave cascade: from one to few to many

Tracking the nonlinear formation of an interfacial wave cascade: from one to few to many | 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 Tracking the nonlinear formation of an interfacial wave cascade: from one to few to many Silke Weinfurtner, Sean Gregory, Silvia Schiattarella, Vitor Barroso Silveira, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6371276/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 A hallmark of far-from-equilibrium systems is the emergence of a spectral cascade, where energy is transferred across lengthscales following a simple power law. The universal nature of this phenomenon has led to advances in a range of disciplines, including climate forecasting [1], foreign exchange trading [2], and the modelling of neurological activity [3]. For many diverse scenarios, the scaling laws of steady states have been successfully predicted by the statistical theory of weak wave turbulence, originally developed by considering the leading order interactions between waves on a fluid surface [4]. However, the predictive power of this theory breaks down in the presence of large amplitudes, high dissipation, and finite-size effects [5]. We offer new insight into these regimes by experimentally tracking the formation of a spectral cascade in an externally driven fluidfluid interface. We resolve individual wave modes and observe their time evolution from one to few to many, a process culminating in a steady state with a spectral density characterised by a power-law scaling. Our findings confirm that interfacial dynamics can be effectively modelled by a weakly nonlinear Lagrangian theory [6, 7], a predictive framework encompassing both underlying wave interaction and emergent behaviours. Such nonlinear interactions are experimentally quantified through statistical correlations, revealing a hierarchy in wave-mixing order that confirms a key assumption of weak wave turbulence theory [4, 8]. The Lagrangian formulation further aids our time-evolution analysis; specific interactions are tracked through time, and we predict the timescale until a cascade emerges. Our findings are transferable to other far-from-equilibrium systems, which we demonstrate by providing a mapping to reheating scenarios following cosmic inflation in the early Universe [9, 10]. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Physics/Fluid dynamics Full Text Additional Declarations There is NO Competing Interest. 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-6371276","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":457132203,"identity":"16f3bc4b-2dc9-4bc9-acfa-9e62f4ec9ee0","order_by":0,"name":"Silke 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