Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases

• DOI: 10.1103/physrevlett.128.114501
• Publication Date: 2022-03-14T15:49:16Z
• Authors: Ryan M. McMullen; Michael C. Krygier; John R. Torczynski; Michael A. Gallis
• Keywords: Kolmogorov microscales; Wavenumber; Stokes number

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