Shockwaves and Local Hydrodynamics; Failure of the Navier-Stokes Equations

TL;DR

This paper investigates the limitations of the Navier-Stokes equations in describing shockwaves in dense fluids, highlighting the importance of nonlocal effects and the failure of classical hydrodynamic models in far-from-equilibrium conditions.

Contribution

It demonstrates the failure of Navier-Stokes equations to accurately model shockwaves in dense fluids and emphasizes the significance of nonlocal averaging in local hydrodynamics.

Findings

Nonlocal hydrodynamic averages are crucial for accurate modeling.

Navier-Stokes equations are incompatible with microscopic reversible dynamics.

Local variables depend heavily on averaging range.

Abstract

Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport properties makes plain the connection between the observed local hydrodynamic variables (like the various gradients and fluxes) and the chosen recipes for defining (or "measuring") those variables. The range over which nonlocal hydrodynamic averages are computed turns out to be much more significant than are the other details of the averaging algorithms. The results show clearly the incompatibility of microscopic time-reversible cause-and-effect dynamics with macroscopic instantaneously-irreversible models like the Navier-Stokes equations.