Direct numerical simulations of supersonic three-dimensional turbulent boundary layers

Abstract: 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 flows demonstrate near-wall self-similarity of the velocity, providing evidence for Morkovin's hypothesis in nonequilibrium 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 decrease, consistent with previous observations in incompressible flows (Lozano-Duran, \textit{et al.} 2019, Moin, \textit{et al.} 1990). 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 turbulent kinetic energy and temperature carrying structures is quantified through structure identification and spectra. Finally, the generalized Reynolds analogy (Zhang, \textit{et al.} 2012) is derived for a transient three-dimensional flow, allowing predictions of the mean temperature from the velocity.