Thermodynamic fluctuations in canonical shock-turbulence interaction

In this work, we use direct numerical simulation and linear interaction analysis to study the thermodynamic field generated by the interaction of a shock wave with homogeneous isotropic turbulence. Fluctuations in density, pressure, temperature and entropy can play an important role in shock-induced mixing, combustion and energy transfer processes. Data from high-fidelity simulations is used to investigate the variation of thermodynamic fluctuations with flow Mach number for a constant turbulent Mach number and Reynolds number. As expected, density, pressure and temperature variances attain large values at the shock, followed by, in general, a decaying profile in the downstream flow. There are, however, cases with nonmonotonic variation with Mach number as well as local peaks in density fluctuations behind the shock. These are explained in terms of the contribution of the post-shock acoustic and entropy modes and their cross-correlation to the thermodynamic variances. Budget of the transport equations reveal interesting insight into the physics governing the trends observed behind the shock wave. It is found that the downstream evolution of the thermodynamic field is determined by competing dilatational and dissipation mechanisms. The dominant mechanisms are identified for a range of conditions and their implication for developing predictive models is highlighted.