Exploring near-continuum turbulent compressible flow in the Taylor-Green vortex

We investigate near-continuum turbulent compressible flow with non-continuum molecular gas dynamics (Direct Simulation Monte Carlo method) and continuum direct numerical simulations of the Navier-Stokes equations. We simulate compressible Taylor-Green vortex flow with polytropic initial conditions at five Mach numbers: 0.3, 0.6, 0.9, 1.2, and 2.0. At each Mach number, we compare kinetic-energy and energy-dissipation histories and velocity fields and spectra to assess the differences between the results from the two methods. The energy-decay histories are nearly identical, but molecular-level fluctuations break the symmetries of the initial condition and produce a different path from the initial nonturbulent flow to the long-time turbulent flow.