Generalization of the viscous stress tensor to the case of non-small gradients of hydrodynamic velocity: a path to numerical modeling of turbulence non-locality

Abstract

Generalization of the Chapman-Enskog method to the case of large gradients of hydrodynamic velocity allowed us to obtain an integral (over spatial coordinates) representation of the viscous stress tensor in the Navier-Stokes equation. In the case of small path lengths of the medium disturbance, the tensor goes over to the standard form, which, as is known, is difficult to apply to the description of tangential discontinuities and separated flows. The obtained expression can allow numerical modeling of the nonlocality of turbulence, expressed by the empirical Richardson t^3 law for pair correlations in a turbulent medium.