Three-dimensional supersonic homogeneous turbulence: A numerical study

A turbulent homogeneous perfect gas with no forcing is computed using the piecewise-parabolic method on a uniform grid of ${256}^3$ zones. The initial rms Mach number is one. The main results are (i) persistence of a quasisupersonic phase with strong density contrasts over several shock formation times; (ii) late appearance of a post-supersonic self-similarly decaying regime in which the total velocity spectrum varies with wave number as ${\mathit{k}}^{\mathrm{-}1}$; and (iii) both shock curvature and velocity gradients are important mechanisms of vorticity production in the first half of the supersonic phase.