Wall-cooling and compressibility effects on high-speed turbulent boundary layers

Aerodynamic drag and heat transfer on high-speed boundary layers are highly influenced by the free-stream Mach number and surface temperature. These two parameters strongly affect the near-wall dynamics, weakening the coupling between velocity and temperature fields that is often leveraged in reduced-order models. In this study, we analyze a numerical database to quantitatively describe Mach number and wall cooling effects in high-speed zero-pressure-gradient turbulent boundary layers using Direct Numerical Simulation. To investigate the individual effect of each parameter, three free-stream Mach numbers (from 2 to 6) and four wall temperature conditions (from adiabatic to very cold walls) are explored, while Re_τ remains fixed. The present database is designed to shed light on the coupling between momentum and temperature fields, with emphasis on the choice of the diabatic parameter Θ [Zhang et al., JFM, 2014] to recover the same flow dynamics at different Mach numbers. Additional analysis on the effect of Mach number and wall-cooling on turbulence anisotropy and separation of turbulence scales allows us to provide a novel view on the physical mechanisms that underlie similar behaviour in certain aspects, while different in others.