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 tau ' x and wall heat flux q & PRIME; 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 tau x ' and q w ' with the aid of the conditional correlation analysis, we identify the asymmetrical deformation of tau ' 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 tau x ' 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 tau x 'and the fluctuating streamwise velocity u' reveals that low-speed streaks related to negative tau x ' are more inclined to the wall than high-speed ones related to positive tau x ' by 4 - 5 , and that the phase lag between negative tau x ' and u' is larger than that between positive tau x' 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. Published under an exclusive license by AIP Publishing.