Wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence, part I: One-point statistics

Abstract

This two-part study investigates the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. In the first part, we focus on their one-point statistics, including the root mean square (r.m.s.), skewness factor (third-order moment), flatness factor (fourth-order moment), and their correlations. By exploiting the direct numerical simulation databases, we found that the r.m.s. of the streamwise wall shear stress and pressure, the skewness factor of all the flow quantities considered, and the flatness factor of streamwise wall shear stress monotonically vary with the friction Mach number (Mτ), while for the rest, the wall heat flux and global temperature parameters should be taken into account as well for a monotonic trend of variation. The correlation coefficients between wall shear stress, pressure, and heat flux fluctuations increase with the Mach number Mτ, suggesting the underlying interactions between dynamic and thermodynamic processes. The distributions of spectra and probability density functions indicate that the increased correlation is induced by the highly intermittent traveling wave packets among the streaky structures, as reflected by the “double-peak” feature of the spectra that gradually emerges with the increasing compressibility effects. The probability density distribution also manifests the alteration of the occurrence of extreme events caused by these structures. By accordingly decomposing the fluctuations with cutoff filtering, it is found that the root mean squares of streamwise wall shear stress and heat flux fluctuations related to the streaky structures are Mach number-independent, while those related to the traveling wave packets monotonically increase with the friction Mach number.