Generalization of the Viscous Stress Tensor to the Case of Non-Small Gradients of Hydrodynamic Velocity: Path to Numerical Modeling of Turbulence Non-Locality

Abstract

A generalization of the Chapman–Enskog method to the case of large gradients of hydrodynamic velocity makes it possible to obtain an integral representation (integral over spatial coordinates) of the viscous stress tensor in the Navier–Stokes equation. In the case of small free paths of disturbances of the medium, the tensor goes over in the standard form, which is known to be difficult to apply to the description of tangential discontinuities and separation flows. The resulting expression can enable numerical modeling of the nonlocality of turbulence, expressed by the empirical Richardson t³ law for pair correlations in turbulent media.