Warm turbulence in the Boltzmann equation

TL;DR

This paper investigates warm turbulence in the Boltzmann equation for a hard sphere gas, revealing a nonequilibrium steady state with energy cascades and providing analytical predictions for temperature based on forcing and dissipation scales.

Contribution

It introduces an analytical framework linking thermodynamic quantities to forcing and dissipation in warm turbulence within the Boltzmann equation context.

Findings

Analytical prediction for system temperature based on forcing and dissipation scales

Numerical simulations support the analytical temperature predictions

Identification of a nonequilibrium steady state characterized by warm turbulence

Abstract

We study the single-particle distributions of three-dimensional hard sphere gas described by the Boltzmann equation. We focus on the steady homogeneous isotropic solutions in thermodynamically open conditions, i.e. in the presence of forcing and dissipation. We observe nonequilibrium steady state solution characterized by a warm turbulence, that is an energy and particle cascade superimposed on the Maxwell-Boltzmann distribution. We use a dimensional analysis approach to relate the thermodynamic quantities of the steady state with the characteristics of the forcing and dissipation terms. In particular, we present an analytical prediction for the temperature of the system which we show to be dependent only on the forcing and dissipative scales. Numerical simulations of the Boltzmann equation support our analytical predictions.