High Schmidt-number turbulent advection and giant concentration fluctuations

نویسندگان

چکیده

We consider the effects of thermal noise on Batchelor-Kraichnan theory high Schmidt-number mixing in viscous dissipation range turbulent flows at sub-Kolmogorov scales. Starting with nonlinear Landau-Lifshitz fluctuating hydrodynamic equations for a binary fluid mixture low Mach numbers, we justify linearization around deterministic Navier-Stokes solution range. For latter adopt standard Kraichnan model, Gaussian random velocity spatially constant strain but white time. Then, following prior work Donev, Fai, and Vanden-Eijnden [J. Stat. Mech.: Theory Exp. (2014) P04004], derive asymptotic Schmidt limiting concentration field, which fluctuations are exactly represented by that is likewise obtain exact spectrum this showing Batchelor prediction viscous-convective unaltered. Thermal dramatically renormalizes bare diffusivity range, effect same as laminar flow thus hidden phenomenologically. However, viscous-diffusive scales below length (typically micron scales) predictions based drastically altered noise. Whereas classical theories predict rapidly decaying spectra either or exponential, ${k}^{\ensuremath{-}2}$ power-law over couple decades starting just length. This corresponds to nonequilibrium giant fluctuations, due imposed variations being advected experimentally well observed quiescent fluids. At higher wave instead goes ${k}^{2}$ equipartition equilibrium molecular fluctuations. out detailed water-glycerol water-fluorescein mixtures. Finally, discuss broad implications applications our methods accessible flows.

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ژورنال

عنوان ژورنال: Physical review research

سال: 2022

ISSN: ['2643-1564']

DOI: https://doi.org/10.1103/physrevresearch.4.023246