Publications

In turbulent flows, kinetic energy is transferred from the largest scales to progressively smaller scales, until it is ultimately converted into heat. The Navier-Stokes equations are almost universally used to study this process. Here, by comparing with molecular-gas-dynamics simulations, we show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations. We investigate decaying turbulence produced by the Taylor-Green vortex and find that in the dissipation range the molecular-gas-dynamics spectra grow quadratically with wave number due to thermal fluctuations, in agreement with previous predictions, while the Navier-Stokes spectra decay exponentially. Furthermore, the transition to quadratic growth occurs at a length scale much larger than the gas molecular mean free path, namely in a regime that the Navier-Stokes equations are widely believed to describe. In fact, our results suggest that the Navier-Stokes equations are not guaranteed to describe the smallest scales of gas turbulence for any positive Knudsen number.

We report flow statistics and visualizations from gas-kinetic simulations using the Direct Simulation Monte Carlo (DSMC) method of compressible turbulent Couette flow over a porous substrate composed of an array of circular cylinders for which the Knudsen number is O(10-1). Comparisons are made with both smooth-wall DSMC simulations and direct numerical simulations of the Navier-Stokes equations for the same conditions. Roughness, permeability, and noncontinuum effects are assessed.