Study of spectral characteristics of a homogeneous turbulent flow

A spectral representation of kinetic energy for a vortex cascade of instability in a compressible inviscid shear flow is considered, and the Rayleigh–Taylor instability is studied. A comparative analysis is given to the spectral decompositions of kinetic energy for both problems. The classical Kolmogorov $-5/3$ power law is proved to hold for developed turbulent flows.