Turbulence via intermolecular potential: A weakly compressible model of gas flow at low Mach number

Abstract

In our recent works, we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial condition, just as observed in nature and experiments. However, we also found that density and temperature behave unrealistically in our inertial flow model. The goal of the current work is to demonstrate the technical possibility of modeling compressible, turbulent flow at a low Mach number where both density and temperature behave in a more realistic fashion. Here, we focus on a new treatment of the pressure variable, which constitutes a compromise between compressible, incompressible, and inertial flow. Similar to incompressible flow, the proposed equation for the pressure variable is artificial, rather than derived directly from kinetic formulation. However, unlike that for incompressible flow, our pressure equation only damps the divergence of velocity, instead of setting it directly to zero. We find that turbulence develops in our weakly compressible model much like it does in the inertial flow model, but density and temperature behave more realistically.