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

In the present study, we investigate two-point statistics of fluctuating streamwise wall shear stress τ′x and wall heat flux q′w 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 τx′ and qw′ with the aid of the conditional correlation analysis, we identify the asymmetrical deformation of τ′x and q′w, 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 τx′ is insensitive to the wall temperature, whereas the spanwise elongated q′w that is closely related to the wall pressure is manifested merely in the cooled-wall case. The cross correlation between τx′ and the fluctuating streamwise velocity u′ reveals that low-speed streaks related to negative τx′ are more inclined to the wall than high-speed ones related to positive τx′ by 4°–5°, and that the phase lag between negative τx′ and u′ is larger than that between positive τx′ 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.