Turbulence in large scale two-dimensional balanced hard sphere gas flow

TL;DR

This paper demonstrates that a two-dimensional balanced hard sphere gas flow model can develop turbulence with a Kolmogorov spectrum, suggesting a potential mechanism for large-scale atmospheric turbulence.

Contribution

The study extends a previous three-dimensional turbulence model to a two-dimensional setting, revealing turbulence emergence in simplified gas flow scenarios.

Findings

Turbulent flows with Kolmogorov spectra develop in 2D gas models.

Large-scale turbulence can arise in purely 2D gas flows.

The model aligns with observed atmospheric turbulence scales.

Abstract

In recent works we developed a model of balanced gas flow where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. Yet, the air density rapidly decays with altitude, roughly by an order of magnitude each 15-20 kilometers. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting.