Turbulent kinetic energy transport in high-speed turbulence subject to wall disturbances

Abstract

Wall disturbances in high-speed turbulent boundary layers induce large-scale motions in the outer region even when the Reynolds number is not sufficiently high for their existence in the case of smooth wall flows. In the present study, we investigate the dynamics of these outer region large-scale motions by exploiting the scale-by-scale energy transport in the spectral space. By scrutinizing the disparity in the budget terms of the turbulent kinetic energy spectra between turbulence over smooth and disturbed walls, we found that the intensification of the large-scale motions in the outer region is statistically correlated with the stronger interaction between the Reynolds stress and the mean shear, i.e. the production term of the turbulent kinetic energy. The corresponding turbulent kinetic energy is then transferred to smaller-scale motions and dissipated by viscosity, whereas the effects of spatial diffusion and mean convection are insignificant and are dimly affected by the wall disturbances. These dynamic processes are roughly irrelevant to the Mach numbers, and processes related directly to the genuine compressibility effects, namely the dilatational motions and mass flux, are trivial. The outer large-scale motions contribute to the skin friction by approximately 19% ∼45% compared with 4% in smooth wall cases in terms of the mean kinetic energy transport, suggesting that the drag increment in turbulent boundary layers in the presence of wall disturbances should be partly attributed to their intensification.