Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence. II. Spectra, correlation and nonlinear interactions

Abstract

Wall shear stress, pressure, and heat flux are of significant importance in engineering applications. In this two-part study, we investigate the compressibility effects on wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence by exploiting direct numerical simulation databases. In Paper I, we primarily deal with the one-point statistics, whereas in this second part, we report the effects of compressibility on the frequency spectra, wavenumber-frequency spectra of these flow quantities, and the two-point cross-correlations between them. It is found that the scaling laws of the spectra at low and high frequencies are retained as those of incompressible flows, whereas the spectra intensities at mid frequencies increase with the enhancement of compressibility effects, which is identified to be related to the ever-predominating traveling wave packets. These wave packets are convected downstream at the same velocity of 0.87Ub as that of pressure fluctuations, higher than that of the streaky structures 0.65Ub (Ub the bulk velocity), and enhance the space and time cross correlation between wall shear stress, pressure, and heat flux fluctuations. By extracting the envelopes of the traveling wave packets and inspecting the time and space correlations between the envelopes and the streaky structures, we found that the emergence of traveling wave packets comes later than the streaky structures, both in time and space. Based on these observations, we provide a depiction of the physical processes regarding the formation and evolution of the traveling wave packets.