Steady Periodic Shear Flow is Stable in Two Space Dimensions . Nonequilibrium Molecular Dynamics vs Navier-Stokes-Fourier Stability Theory -- A Comment on two Arxiv Contributions

TL;DR

This paper compares stability predictions of shear flows from Navier-Stokes-Fourier theory with molecular dynamics simulations, highlighting discrepancies in two-dimensional cases where molecular dynamics shows stability contrary to theoretical predictions.

Contribution

It demonstrates that two-dimensional steady shear flows are stable in molecular dynamics simulations, contradicting the instability predicted by Navier-Stokes-Fourier stability analysis.

Findings

Molecular dynamics simulations show stable shear flows in 2D.

Navier-Stokes-Fourier theory predicts instability in 2D shear flows.

Discrepancy between theoretical predictions and simulation results remains unexplained.

Abstract

Dufty, Lee, Lutsko, Montanero, and Santos have carried out stability analyses of steady stationary shear flows. Their approach is based on the compressible and heat conducting Navier-Stokes-Fourier model. It predicts the unstable exponential growth of long-wavelength transverse perturbations for both two- and three-dimensional fluids. We point out that the patently-stable two-dimensional periodic shear flows studied earlier by Petravic, Posch, and ourselves contradict these predicted instabilities. The stable steady-state shear flows are based on nonequilibrium molecular dynamics with simple thermostats maintaining nonequilibrium stationary states in two space dimensions. The failure of the stability analyses remains unexplained.