Direct numerical simulation of supersonic and hypersonic turbulent boundary layers at moderate-high Reynolds numbers and isothermal wall condition

We study the structure of high-speed zero-pressure-gradient turbulent boundary layers up to friction Reynolds number $Re_{\tau } \approx 2000$ using direct numerical simulation Navier–Stokes equations. Both supersonic and hypersonic conditions with nominal free-stream Mach numbers $M_{\infty }=2$ , }=5.86$ heat transfer at wall are considered. The present simulations extend database currently available for wall-bounded flows, enabling us explore high-Reynolds-number effects even in regime. first analyse instantaneous fields characterize both velocity temperature fluctuations. In all cases elongated strips uniform (superstructures) observed outer portion layer, characterized by a clear association between low-/high-speed momentum high/low streaks. results highlight important deviations from typical organization inner region adiabatic layers, revealing that near-wall streaks disappear strongly non-adiabatic flow cases. also focus on structural properties regions streamwise (De Silva, Hutchins & Marusic, J. Fluid Mech. vol. 786, 2016, pp. 309–331) confirming presence such zones regime high existence similar field. accuracy different compressibility transformations temperature–velocity relations is assessed extending their range validation moderate/high numbers. Spanwise spectral densities fluctuations various distances have been calculated energy content size eddies across layer. Finally, we propose revised scaling characteristic length scales, based local mean shear computed according recent theory Griffin, Fu Moin [ Proc. Natl Acad. Sci. USA 118 (34)].