Modeling of turbulent fluid motion based on the Boussinesq hypothesis. Overview

A mathematical simulation of a turbulent flow in a compressible and incompressible viscous fluid is considered using the example of the simplest model of turbulent motion, obtained as a result of averaging the Navier-Stokes equations from Reynolds and Favre in conjunction with the Boussinesq hypothesis on the presence of turbulent viscosity. Algorithms for averaging the Navier-Stokes equations for a compressible and incompressible fluid are given. Appropriate equations for the averaged and pulsating field parameters for incompressible and compressible liquids are given. The results obtained are useful in the design of a new type of radiator, described in [1, 2], when operating in the turbulent regime of fluid motion.