Triadic energy cascades and linear amplification mechanisms in supersonic turbulent boundary layers over curved walls

Abstract

Direct numerical simulations are performed to investigate supersonic turbulent boundary layers subjected to continuous concave and convex surface curvatures. Scale-resolved spectral turbulent kinetic energy (TKE) budgets, triadic energy-transfer bispectra, spectral proper orthogonal decomposition (SPOD), and global resolvent analysis are employed to elucidate the effects of compressibility and pressure gradients, and to distinguish the linear and nonlinear mechanisms at play. Over concave walls, the destabilizing curvature enhances pressure-strain redistribution, shifting near-wall turbulence toward a two-component state, and induces a shear-driven outer-layer production peak at low spanwise wavenumbers. Bispectral and SPOD analyses reveal that this outer-layer energy feeds a structured, multi-step triadic transfer toward fundamental large-scale and spanwise-uniform modes, which physically manifests as streamwise vortex breakdown rather than a three-dimensional inverse cascade. Global resolvent analysis further demonstrates that while nonlinear triadic interactions select the dominant scale amplitudes, the spatial topology of these coherent structures is dictated by linear mean-flow receptivity and spatially developing convective instabilities. Conversely, over convex walls, stabilizing curvature and dilatation attenuate pressure fluctuations and suppress pressure-strain redistribution, breaking the near-wall turbulent cycle and trapping energy within elongated, one-component streamwise streaks, while a localized resolvent wavemaker energizes the downstream recovery region.