Positive and negative pairs of fluctuating wall shear stress and heat flux in supersonic turbulent boundary layers

Abstract

The negative and positive fluctuations of wall shear stress τ′x and wall heat flux q′w can be related to the wall-attached paired up large-scale velocity and temperature streaks. It is justifiable to infer the spatially paired-up coexistence of those wall flow quantities. The present study aims at testifying this hypothesis. We establish such relations between the negative and positive wall shear stress by exploiting a direct numerical simulation database over heated and cooled walls at the friction Reynolds number of 800 and the Mach number of 2.25. The clustering method is adopted for the search of the in-pair structures. It is found that the τx- and qw-structures are less self-similar for flows over cold walls. As they become wider, the τx-structures are increasingly more streamwise stretched, while the trend is reversed for qw-structures. τx-structures of opposite signs are paired up and aligned in the spanwise directions as the wall-attached streamwise velocity, and are left behind by streamwise rollers. The relative position between qw-structures of opposite signs, on the other hand, is sensitive to the wall temperature. Scrutinizing the statistical structures, we elucidate that such spatial coherence is determined by the meandering of velocity streaks that yields strong streamwise gradients of the streamwise velocity.