  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.
