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

2012/03/07 by Hoover, Wm. G., Hoover, Carol G.
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1203.1374

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.

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