This study investigates the effect of Reynolds number on unsteady buffet characteristics of the OAT15A supercritical airfoil under transonic conditions (Ma = 0.73, AOA = 3.5°) using DDES based on the SST k-ω turbulence model coupled with the γ-Reθ transition model. Results show that, compared with fully turbulent conditions, the free-transition cases exhibit a more downstream shock position and higher lift. Under fully turbulent conditions, higher Reynolds numbers drive the shock downstream and enhance its stability. Under free-transition conditions, the shock moves downstream at low Reynolds numbers but shifts upstream at high Reynolds numbers due to changes in the transition location. During the unsteady buffet cycle at low Reynolds numbers, the lift increases as the shock moves downstream and the separation region shrinks. The lift reaches its maximum when the separation is minimal, corresponding to a quiet flow state with weak acoustic emission. As the lift decreases, a large separation region forms behind the shock, forcing the shock upstream and reducing the lift to its minimum. At high Reynolds numbers, the buffet cycle changes: the shock becomes more stable; trailing-edge vortex shedding intensifies; lift oscillation amplitude decreases; and buffet frequency increases.

Accurate prediction of boundary layer transition in hypersonic flows is a critical challenge due to the coexistence of multiple instability mechanisms and their sensitivity to flow conditions. In this work, we propose a physics-informed multiscale attention wavelet neural operator (PIMAWNO) as a surrogate for the linear parabolized stability equations (LPSEs). The method employs a dual-operator collaborative training strategy, in which a perturbation profile operator and a streamwise wavenumber operator are trained on a high-fidelity database while exchanging information through physical normalization conditions. Symlet-9 wavelets are identified as the optimal basis, offering the lowest mean square error across training and testing datasets, with error levels consistently one to two orders of magnitude smaller than perturbation amplitudes. Model performance is evaluated on four canonical instabilities: traveling Mack mode, second mode, cross-flow mode, and centrifugal mode, with perturbation profiles and N-factor curves. Across all cases, PIMAWNO predictions closely reproduce LPSE solutions, accurately capturing both the spatial distribution and downstream amplification of disturbances. Absolute error analysis reveals that discrepancies are concentrated in regions of steep gradients, such as near-wall temperature peaks in the Second mode or spanwise velocity growth in the Centrifugal mode. These results confirm the potential of PIMAWNO as a robust, wavelet-enhanced surrogate model for LPSE, enabling efficient and accurate prediction of hypersonic boundary layer transition and providing a foundation for future stability-based transition prediction strategies.

The study in this paper investigates the effects of combined nose tip wall cooling and porous surfaces on boundary layer transition over a 7° half-angle sharp cone under Mach 6 flow conditions, using a combination of wind tunnel experiments and parabolized stability equations analysis. Experimental results indicate that nose tip cooling promotes the emergence of high-frequency instability modes and advances the onset of boundary layer transition compared to the uncooled wall condition. N-factor analysis further corroborates the destabilizing effect of nose tip cooling, showing good agreement with the experimental observations. To achieve more effective control of broadband instability disturbances, a combined control strategy is proposed, in which a porous surface is applied downstream of the cooled region to suppress the growth of high-frequency modes. The results demonstrate that, compared with wall cooling alone, the combined approach significantly reduces the growth rates of broadband disturbances and delays the onset of transition. Bispectral analysis further reveals that the integrated control strategy effectively suppresses nonlinear interactions within the hypersonic boundary layer, including both high-frequency harmonic interactions and low- and high-frequency coupling. In contrast, single control strategies mitigate only one type of nonlinear interaction, thereby underscoring the superior performance of the combined approach.