Macroscopic turbulent flow via hard sphere potential

Abstract

In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety of different potentials. In this work, we use the same hypothesis to develop new fluid mechanics equations which model turbulent gas flow on a macroscopic scale. The main difference between our approach and the conventional formalism is that we avoid replacing the potential interaction between particles with the Boltzmann collision integral. Due to this difference, the velocity moment closure, which we implement for the shear stress and heat flux, relies upon the high Reynolds number condition, rather than the Newton law of viscosity and the Fourier law of heat conduction. The resulting system of equations of fluid mechanics differs considerably from the standard Euler and Navier-Stokes equations. A numerical simulation of our system shows that a laminar Bernoulli jet of an argon-like hard sphere gas in a straight pipe rapidly becomes a turbulent flow. The time-averaged Fourier spectra of the kinetic energy of this flow exhibit Kolmogorov's negative five-thirds power decay rate.