Non-equilibrium three-dimensional supersonic boundary layers*

Studies on compressible, wall-bounded turbulent flows largely focus on canonical two-dimensional flows, like boundary layers and channels. In this work, the results of direct numerical simulations of a compressible turbulent channel flow subjected to sudden spanwise pressure gradients at different initial Reynolds and Mach numbers are presented. This study focuses on the transient response during which the channel exhibits three-dimensionality in the mean statistics. During this transient the turbulent kinetic energy decreases, consistent with previous observations in incompressible flow (Lozano-Duran, A., et. al. (2019), Moin, P. et. al. (1990)). The temperature fluctuations also decrease, despite the net increase in the mean temperature. For large spanwise to streamwise pressure gradient ratios, a non-monotonic mean temperature can be observed that creates a positive correlation between the wall-parallel velocities and the temperature fluctuations near the wall and a negative correlation away from the wall. For smaller ratios, the mean temperature is monotonic, and this correlation is positive across the channel. The behavior in the turbulent fluctuations can be explained by tracking the production terms in the kinetic energy, Reynolds stress, and velocity-temperature variance evolution equations. Finally, the validity of Morkovin's hypothesis in this temporal-three-dimensional flow will also be assessed through comparisons with the corresponding incompressible regime.