Supersonic homogeneous turbulence

Abstract

Supersonic turbulence is observed in the giant molecular clouds in the galactic disk and may also occur at re-entry of space shuttles. Numerical simulations in three dimensions concerning compressible homogeneous non-stationary flows using the fluid equations with the Navier-Stokes formulation, a hyperviscosity method, and new simulations of the Euler equations using the PPM code are presented. Results are for random flows at a rms Mach number of unity on uniform grids with periodic boundary conditions. Through visualization and analysis of the fluid simulations, we conclude that: i) shock waves and shock intersections play an important role in the transfer of energy from long to short wavelengths. Weak shocks survive for several T _{a c}, where T _{a c} is the acoustic time of the energy containing modes in the initial state. In the context of our decay problems, vorticity is concentrated in filaments, and not sheets, within a few acoustic times. Whereas in two dimensions eddies tend to slowly merge over many T _{a c}, in 3-D vortex filaments break up into short filaments within a few T _{a c}; ii) three temporal phases are identified in the evolution of the flow, onset and formation of shocks, quasi-supersonic phase with many interacting shocks, and post-supersonic phase with a velocity spectrum flatter than that of Kolmogorov.