On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows

The near-wall structures and statistics of fluctuating pressure (p ') in compressible turbulent channel flows (CTCF) with isothermal walls have been investigated by direct numerical simulations. Two typical cases for high bulk Mach number Ma = 3.83 and low one Ma = 1.56 are considered. A novel type of near-wall pressure structures named alternating positive and negative structures (APNS) is found in the high-Ma case based on the comprehensive analysis of spectra and dynamic mode decomposition of p '. These APNS of p ' are identified to have the streamwise and spanwise length scales of (lambda (x)/h, lambda (z)/h) approximate to (0.9, 1.5), where h is the channel half-height, and prefer to inhabit the low-speed wall streaks. It is also verified via a pressure splitting method that the APNS of p ' are dominated by the compressibility effects. Based on the linear stability analysis, the APNS of p ' can be intimately related to a linear stability eigenmode of the high-Ma CTCF and are sustained by the transient growth mechanism as the disturbances of the APNS length scales. Furthermore, these APNS of p ' offer an extra mechanism to generate the near-wall p ' for the high-Ma case. Moreover, it is found that the APNS of p ' have a dominating effect on the pressure-dilatation correlation and the production of Reynolds shear stress. The present study may provide a reliable way to achieve a better understanding and modeling of compressibility effects in the wall-bounded turbulence of high Ma.