Creation of turbulence in polyatomic gas flow via an intermolecular potential

TL;DR

This paper introduces a new kinetic model for polyatomic gases incorporating intermolecular potentials, demonstrating that such interactions can induce turbulence in inertial flow regimes, with numerical evidence showing Kolmogorov-like spectra.

Contribution

It develops a novel kinetic equation with a mean field potential for polyatomic gases and shows turbulence can arise from intermolecular forces in high Reynolds number flows.

Findings

Intermolecular potential induces turbulence in gas flow.

Flow exhibits Kolmogorov's power decay in energy spectra.

Model applicable to various gases regardless of thermodynamic specifics.

Abstract

We develop a tractable interaction model for a polyatomic gas, whose kinetic equation combines a Vlasov-type mean field forcing due to an intermolecular potential, and a Boltzmann-type collision integral due to rotational interactions. We construct a velocity moment hierarchy for the new kinetic equation, and find that, under the high Reynolds number condition, the pressure equation becomes decoupled from the angular momentum and stress. For the heat flux, we propose a novel closure by prescribing the specific heat capacity of the gas flow. Setting the specific heat capacity to that of a constant-pressure process leads to the system of equations for a balanced flow, where the momentum transport equation contains the mean field forcing, which is an averaged effect of the intermolecular potential. Remarkably, the balanced flow equations do not contain any information about internal thermodynamic properties of the gas, and are thereby applicable to a broad range of different gases. We conduct numerical simulations for an air-like gas at normal conditions in the inertial flow regime, where the pressure is constant throughout the domain. We find that the presence of the intermolecular potential produces a distinctly turbulent flow, whose time-averaged Fourier spectra of the kinetic energy and temperature exhibit Kolmogorov's power decay.