A Collision-Based Kinetic Model for the Molecular Seeding and Amplification of Turbulence

A Binomial Random-Walk Framework Quantifying Molecular Collision-Induced Fluctuations in Inertial-Range Eddies | 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 A Binomial Random-Walk Framework Quantifying Molecular Collision-Induced Fluctuations in Inertial-Range Eddies Tristan Barkman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7134383/v3 This work is licensed under a CC BY 4.0 License Status: Posted Version 3 posted You are reading this latest preprint version Show more versions Abstract Pure molecular velocity increments are individually short-lived and are viscously dissipated on timescales many orders of magnitude shorter than Kolmogorov turnover times, so the classical continuum assumption that molecular-scale fluctuations are dynamically irrelevant is untenable when asking how perturbations are seeded at dissipation scales. Treating molecular collisions as a three-dimensional binomial random walk shows that zero-mean collision steps accumulate Brownian-style variance that survives continuum averaging (which removes the mean but preserves second moments), producing a finite rms velocity at dissipation scales on the order of mm/s. These irreducible microscale fluctuations at the Kolmogorov scale provide a persistent population of seed perturbations. In high–Reynolds-number flows, Lagrangian strain and positive finite-time Lyapunov exponents selectively and exponentially amplify those seeds that experience favorable stretching, converting them into microscale eddies that then participate in the upscale cascade to fully developed inertial-range eddies and enhanced eddy diffusivity. The analysis, therefore, connects angstrom-scale collisional physics to macroscopic turbulence and indicates that molecular-seed statistics should be incorporated into closure models and validated with targeted DNS/MD and micro-PIV experiments. Plasma and Fluids random walk turbulence Brownian motion spontaneous stochasticity Full Text Additional Declarations The authors declare no competing interests. Supplementary Files Supplement.docx Supplementary Materials Cite Share Download PDF Status: Posted Version 3 posted You are reading this latest preprint version Show more versions 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. 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