Direct numerical simulations of supersonic three-dimensional turbulent boundary layers

Supersonic turbulent channels subjected to sudden spanwise acceleration at initial friction Reynolds numbers of approximately 500 and different Mach numbers are studied through direct numerical simulations. The response to the spanwise acceleration creates a transient period where the flow exhibits three-dimensionality in the mean statistics. This enables a detailed study of the thermal transport and development of velocity transformations and Reynolds analogies for compressible turbulent flows in swept-like conditions. Extensions of velocity transformations to three-dimensional (3-D) flows demonstrate near-wall self-similarity of the velocity, providing evidence for Morkovin’s hypothesis in non-equilibrium conditions. A similarity solution for the spanwise velocity, valid during the initial transient, is also presented. During the transient, both the thermal fluctuations and turbulent kinetic energy (TKE) decrease, consistent with previous observations in incompressible flows (Lozano-Durán et al. 2020 J. Fluid Mech. 883, A20, Moin et al. 1990 Phys . Fluids A: Fluid Dyn . 2, 1846–1853). For sufficiently strong spanwise acceleration, $Q_{3}$ $(+T',+v')$ and $Q_{1}$ $(-T',-v')$ events become more significant than sweep and ejections across the channel, creating changes in sign in the velocity–temperature covariances. The temporal evolution of the orientation and sizes of the TKE and temperature-carrying structures is quantified through structure identification and spectra. Finally, the generalized Reynolds analogy (Zhang et al. 2012 Phys. Rev. Lett . 109, 054502) is derived for a transient 3-D flow, allowing predictions of the mean temperature from the velocity.