Kovasznay Mode Decomposition of Velocity-Temperature Correlation in Canonical Shock-Turbulence Interaction

The correlation coefficient RuT between the streamwise velocity and temperature is investigated for the case of canonical shock-turbulence interaction, motivated by the fact that this correlation is an important component in compressible turbulence models. The variation of RuT with the Mach number, the turbulent Mach number, and the Reynolds number is predicted using linear inviscid theory and compared to data from DNS. The contributions from the individual Kovasznay modes are quantified. At low Mach numbers, the peak post-shock RuT is determined by the acoustic mode, which is correctly predicted by the linear theory. At high Mach numbers, it is determined primarily by the vorticity and entropy modes, which are strongly affected by nonlinear and viscous effects, and thus less well predicted by the linear theory.