SPECTRAL LAWS FOR THE COMPRESSIBLE ISOTROPIC TURBULENCE

Scaling arguments are applied directly to the Navier-Stokes equations with the isentropic-flow stipulation in conjunction with the scale-invariance condition on the mean rate of kinetic energy dissipation to derive the spectral law for the three-dimensional compressible isotropic turbulence when the random sound field is weak. For the special case with isothermal flow, the present result also reduces to the Kadomtsev-Petviashvili spectral law approximately k-2. We Will then address the nature of compressibility effects on the classical turbulent spectrum.