The mechanics of turbulence formation via an interaction potential: A simple two-particle model

Rafail V. Abramov

Published 2020-11-19Version 1

In a recent work, we proposed the hypothesis that the turbulence in fluids could be produced by fluid particles interacting via a potential (for example, an interatomic potential at short ranges, and the electrostatic potential at long ranges). Here, we examine the basic mechanics of turbulence formation by studying a simple model which consists of only two particles, which interact via a potential. We start with the equations of motion for this pair of particles, then consider the corresponding Liouville equation for these dynamics, and subsequently derive the velocity moment transport equations. We close these equations using the hydrostatic and thermostatic approximations, and arrive at the closed equation for the velocity variable alone. We show that the velocity equation in the Fourier space can form time-periodic patterns under the potential forcing, coupled to a strong large scale flow. We find that the scaling of the equilibrium states of these patterns is consistent with the Kolmogorov energy scaling.