Anomalous Pressure in Fluctuating Shear Flow

TL;DR

This paper explores how pressure behaves in fluctuating shear flows, revealing anomalous scaling laws and the influence of system size and shear rate on pressure's intensive or non-intensive nature.

Contribution

It derives new forms of pressure dependence in fluctuating hydrodynamics under shear, highlighting the transition between non-intensive and intensive regimes based on system parameters.

Findings

Pressure is non-intensive for small λ due to long-range correlations.

Pressure becomes intensive for large λ, with non-equilibrium correction proportional to S^{3/2}.

The results connect to previous findings by Kawasaki and Gunton (1973).

Abstract

We investigate how the pressure in fluctuating shear flow depends on the shear rate $S$ and on the system size $L$ by studying fluctuating hydrodynamics under shear conditions. We derive anomalous forms of the pressure for two limiting values of the dimensionless parameter $\lambda=SL^2/\nu$, where $\nu$ is the kinematic viscosity. In the case $\lambda \ll 1$, the pressure is not an intensive quantity because of the influence of the long-range spatial correlations of momentum fluctuations. In the other limit $\lambda \gg 1$, the long-range correlations are suppressed at large distances, and the pressure is intensive. In this case, however, there is the interesting effect that the non-equilibrium correction to the pressure is proportional to $S^{3/2}$, which was previously obtained with the projection operator method [K. Kawasaki and J. D. Gunton, Phys. Rev. {\bf A 8}, 2048, (1973)].