Effects of wall temperature on two-point statistics of the fluctuating wall shear stress and heat flux in supersonic turbulent boundary layers

Abstract

In the present study, we investigate two-point statistics of fluctuating streamwise wall shear stress [Formula: see text] and wall heat flux [Formula: see text] by exploiting a direct numerical simulation database of supersonic turbulent boundary layers over a heated wall and a cooled wall at the friction Reynolds number around 800. By separately investigating positive and negative families of [Formula: see text] and [Formula: see text] with the aid of the conditional correlation analysis, we identify the asymmetrical deformation of [Formula: see text] and [Formula: see text], reminiscent of and ascribed to the asymmetrical deformations of sweeps and ejections events. The degree of such asymmetry is alleviated by the lower wall temperature. The spatial orientation of [Formula: see text] is insensitive to the wall temperature, whereas the spanwise elongated [Formula: see text] that is closely related to the wall pressure is manifested merely in the cooled-wall case. The cross correlation between [Formula: see text] and the fluctuating streamwise velocity u′ reveals that low-speed streaks related to negative [Formula: see text] are more inclined to the wall than high-speed ones related to positive [Formula: see text] by [Formula: see text], and that the phase lag between negative [Formula: see text] and u′ is larger than that between positive [Formula: see text] and u′ except in the near-wall region. Such a difference is proportional to the wall distance and should be considered for models predicting near-wall and wall quantities using signals in the logarithmic layer.