On the validity of the continuum approximation in high Reynolds number turbulence

Abstract

It is shown that the inverse Kolmogorov-Knudsen number, defined as the ratio of the Kolmogorov length scale to the molecular mean-free path increases with turbulence Reynolds number, at constant turbulent Mach number. Despite the increasing range of turbulence spatial scales as the Reynolds number increases, in turbulence, the continuum assumption and the Navier-Stokes equations are an increasingly good approximation as the Reynolds number increases.