Consistent initial conditions for the DNS of compressible turbulence

Relationships between diverse thermodynamic quantities appropriate to weakly compressible turbulence are derived. It is shown that for turbulence of a finite turbulent Mach number there is a finite effect of compressibility. A methodology for generating initial conditions, consistent with finite Mach number, for the fluctuating pressure, density, and dilatational velocity is given. Use of these initial conditions gives rise to a smooth development of the flow, in contrast to cases in which these fields are specified arbitrarily or set to zero. Comparisons of the effect of different types of initial conditions are made using direct numerical simulation of decaying isotropic turbulence.