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The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 τ x ′ and q w ′ 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 τ 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 τ x ′ and the fluctuating streamwise velocity u′ reveals that low-speed streaks related to negative τ x ′ are more inclined to the wall than high-speed ones related to positive τ x ′ by 4 ° – 5 ° , and that the phase lag between negative τ x ′ and u′ is larger than that between positive τ 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. [ABSTRACT FROM AUTHOR]

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon ["Extremely high wall-shear stress events in a turbulent boundary layer," J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. ["Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions," J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions. [ABSTRACT FROM AUTHOR]