Abstract
The spectral transport equations of turbulence kinetic and internal energy (TKE and TIE) are rigorously derived in the compressible turbulent flows, exhibiting a full structural similarity in terms of two-point correlations of velocity and a sound-speed-like variable. The scale dependence of TKE and TIE flow across space and scales, and among components is revealed comprehensively in a similar manner, in hypersonic turbulent boundary layers. Special attention is paid to the effect of wall cooling on the energy evolution, which is observed to exist throughout the boundary layer primarily by means of modifying the small-scale motions.
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