Energy and spectral dynamics in decaying compressible turbulence

The statistical properties of decaying compressible turbulence are investigated by direct numerical simulations of flow in a periodic cube. Starting with fully developed turbulence for various microscale Reynolds numbersR, rms Mach numbersM, and small- and large-scale compressive ratiosr_CS andr_CL, we find that the kinetic energy exhibits an exponential decay in time. Interactions between the compressive and rotational components of kinetic energy are weaker than self-interactions of the respective components. The energy spectrum of rotational component obeys the same Kolmogorov similarity law as for incompressible turbulence and forced compressible turbulence. The form of the energy spectrum of the compressive component, on the other hand, depends strongly onM. As the turbulence decays freely,R andM decrease in time butr_CS andr_CL tend to some universal values.