The temporal scaling laws of compressible turbulence

This paper proposes temporal scaling laws of the density-weighted energy spectrum for compressible turbulence in terms of dissipation rate, frequency and the Mach number. The study adopts the incomplete similarity theory in the scaling analysis of compressible turbulence motion. The investigation shows that the temporal Eulerian and Lagrangian energy spectra approach the -5/3 and -2 power laws when the Mach number M tends to reach unity and infinity, respectively.