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 element of compressibility. A methodology for generating initial conditions for the fluctuating pressure, density and dilatational velocity is given which is consistent with finite Mach number effects. 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.