Nonlocal generalization of the Chapman-Enskog method and hydrodynamic equations. Nonlocal vorticity transport in a turbulent medium

Abstract

The results from [Fluid Dyn 61, 20 (2026)], concerning the generalized Chapman-Enskog method and a nonlocal (i.e., non-diffusive, spatially integral) viscous stress tensor in the Navier-Stokes equation, are extended to the case of arbitrary gradients of not only hydrodynamic velocity but also temperature. The resulting equations simplify the description of tangential discontinuities and separated flows. For the specific case of an incompressible medium, a nonlocal vorticity transport equation is derived that is structurally identical to the Biberman-Holstein equation for resonant radiation transport in plasmas and gases. A power-law form has been determined for the velocity distribution function of long-free-path vorticity carriers that satisfies empirical Richardson t^3 law for the mean square of relative separation of a pair of particles in a turbulent liquid or gaseous medium.