New exact solution of the Navier-Stokes equations for turbulence in a compressible medium

TL;DR

This paper presents a novel exact solution to the Navier-Stokes equations for compressible turbulence, providing a closed-form description of statistical moments and addressing the closure problem in turbulence theory.

Contribution

It introduces a new exact solution for compressible flows with low shear viscosity, enabling a closed description of velocity moments and advancing turbulence modeling.

Findings

Derived an exact solution for compressible turbulence.

Provided a closed-form evolution of statistical velocity moments.

Addressed the closure problem in turbulence theory.

Abstract

A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the evolution of statistical moments of velocity is obtained, thereby bypassing the closure problem in the theory of turbulence.