The Spatial Scaling Laws of Compressible Turbulence

The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectrum and showed that, within the initial subrange, both energy spectrums approach the -5/3 power law of the wavenumber, when the Mach number $M$ tends to be naught, unity and infinity, respectively.