Conditionally averaged skin-friction decomposition on the wall-attached Reynolds stress structure in supersonic turbulent boundary layers

The coherent structures in supersonic turbulent boundary layers, particularly wall-attached Reynolds stress structures (RSS), exhibit significant correlations with skin-friction drag generation. However, the intrinsic coupling between streamwise motions, wall-normal motions, and evolutionary processes of RSS has obscured the precise mechanisms governing their scale-dependent interactions. This study investigates the generation mechanisms of high/low skin friction in a supersonic turbulent boundary layer via direct numerical simulations. A novel methodology combining a time-resolved clustering method and conditionally averaged skin-friction decomposition is employed, focusing on wall-attached RSS (Q2 ejections and Q4 sweeps) of varying wall-normal scales ( $l_y^+$ ), which decomposes the skin-friction coefficient into contributions from streamwise ( $C_{\kern-2.5pt f}^{M_x}$ ), wall-normal ( $C_{\kern-2.5pt f}^{M_y}$ ) and spanwise ( $C_{\kern-2.5pt f}^{M_z}$ ) motions, etc. Results show that $C_{\kern-2.5pt f}^{M_y}$ dominates friction generation, while $C_{\kern-2.5pt f}^{M_z}$ attenuates it. A significant scale dependence is revealed: $C_{\kern-2.5pt f}^{M_x}$ counteracts friction for large-scale structures, contrary to its effects at smaller scales. These three terms reflect the influence of momentum transport by RSS on skin friction, which is specifically manifested in the convective acceleration. The unsteady term ( $C_{\kern-2.5pt f}^U$ ) partially offsets $C_{\kern-2.5pt f}^{M_x}$ , linked to structural evolution phases: growth dominates for small scales, and decay for large scales. These findings elucidate the scale-dependent momentum transport mechanisms governing skin friction, providing insights for drag-reduction strategies in high-speed flows.