Fluctuating hydrodynamics in a vertically vibrated granular fluid with gravity

TL;DR

This study explores hydrodynamic fluctuations in a vertically vibrated 2D granular fluid under gravity, revealing that velocity fluctuations behave similarly to equilibrium fluids but with unique non-equilibrium characteristics captured by an effective fluctuating hydrodynamics model.

Contribution

It introduces an effective fluctuating hydrodynamics framework that accounts for non-equilibrium velocity fluctuations in a vibrated granular fluid with gravity.

Findings

Autocorrelation decay is exponential, indicating vorticity diffusion similar to equilibrium fluids.

Velocity structure factor deviates from equilibrium constant behavior and is well modeled by two noise terms.

Fluctuations are measured in horizontal layers smaller than hydrodynamic lengths, approximating homogeneity.

Abstract

We investigate hydrodynamic fluctuations in a 2D granular fluid excited by a vibrating base and in the presence of gravity, focusing on the transverse velocity modes. Since the system is inhomogeneous, we measure fluctuations in horizontal layers whose width is smaller than the characteristic hydrodynamic lengths: they can be considered as almost-homogeneous subsystems. The large time decay of autocorrelations of modes is exponential and compatible with vorticity diffusion due to shear viscosity, as in equilibrium fluids. The velocity structure factor, which strongly deviates from the equilibrium constant behavior, is well reproduced by an effective fluctuating hydrodynamics described by two noise terms: the first associated with vorticity diffusion and the second with the local energy exchange, which have internal and external character, respectively.