Stability of Uniform Shear Flow

TL;DR

This paper investigates the stability of idealized shear flow at long wavelengths, combining hydrodynamic analysis, kinetic modeling, Monte Carlo simulations, and molecular dynamics to understand the onset and nature of flow instabilities.

Contribution

It extends stability analysis of shear flow to larger shear rates using kinetic equations and validates findings with simulations, revealing the development of non-uniform quasi-stationary states.

Findings

Identified instability at long wavelengths for any finite shear rate.

Hydrodynamic and kinetic models agree on instability behavior for short times.

Long-term simulations show the flow evolves into a non-uniform quasi-stationary state.

Abstract

The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at any finite shear rate for sufficiently long wavelength perturbations. The analysis is extended to larger shear rates using a low density model kinetic equation. Direct Monte Carlo Simulation of this equation is computed with a hydrodynamic description including non Newtonian rheological effects. The hydrodynamic description of the instability is in good agreement with the direct Monte Carlo simulation for $t < 50t_0$, where $t_0$ is the mean free time. Longer time simulations up to $2000t_0$ are used to identify the asymptotic state as a spatially non-uniform quasi-stationary state. Finally, preliminary results from molecular dynamics simulation showing the instability are presented and discussed.