Mesoscopic Theory of Critical Fluctuations in Isolated Granular Gases

TL;DR

This paper develops a mesoscopic hydrodynamic theory to describe energy fluctuations in isolated granular gases near clustering instability, predicting divergence and scaling behaviors confirmed by simulations.

Contribution

It introduces a novel theoretical framework focusing on vorticity fluctuations to explain energy fluctuations in granular gases near criticality.

Findings

Energy fluctuations are governed by vorticity fluctuations.

Predicted power-law divergence of fluctuation moments.

Theoretical results agree with simulation data.

Abstract

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only, that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out.