Quantitative analysis of fluctuating hydrodynamics in uniform shear flow

Abstract

Many theoretical predictions in fluctuating hydrodynamics under uniform shear flow have lacked precise quantitative verification because assessing the impact of analytical approximations is difficult and microscopic particle-based simulations have inherent limitations. To address this problem, we perform direct numerical simulations of the fluctuating Navier-Stokes equations with shear-periodic boundary conditions. We provide a decisive validation of two seminal frameworks: the Lutsko-Dufty theory for nonequilibrium long-range correlations, and the dynamic renormalization group (RG) theory pioneered by Forster, Nelson, and Stephen for anomalous transport. First, we demonstrate that the predictions of the Lutsko-Dufty theory are quantitatively valid from the viscous-dominated, short-wavelength regime to the shear-dominated, long-wavelength regime. Second, we test the quantitative predictive capability of the dynamic RG approach and show that the one-loop RG prediction is accurate even when the renormalization correction is comparable to the bare viscosity, a regime in which conventional perturbation theory fails. Our findings solidify the foundations of these classical theories, paving the way for quantitative analyses using fluctuating hydrodynamics.