High-frequency instabilities in supersonic compression-ramp flow

We consider high Reynolds number supersonic flow over a compression ramp in the triple-deck formulation. Previous studies of compression-ramp stability have shown rapid growth of high-frequency disturbances in initial-value computations; however, no physical or numerical origin has yet been identified robustly. By considering linear perturbations to steady compression-ramp solutions, we show that instabilities observed in previous studies do not have a growth rate that is described by the integral eigenrelation of Tutty & Cowley (J. Fluid Mech., vol. 168, 1986, pp. 431-456) for a (long-wave) Rayleigh instability. We solve both the temporal and spatial instability problems in the limit of asymptotically large wavenumber K (or equivalently frequency) and show that the growth rate of the instability remains o(K), being dominated by higher-order terms in the expansion at moderate ramp angles.

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In this study, we investigate high Reynolds number supersonic flow over a compression ramp in the triple-deck formulation. Previous studies have shown rapid growth of high-frequency disturbances in initial-value computations, but the physical or numerical origin of these instabilities remains unidentified. By analyzing linear perturbations and considering the integral eigenrelation proposed by Tutty and Cowley, we demonstrate that the observed instabilities do not follow the expected growth rate. We solve both temporal and spatial instability problems at large wavenumbers and find that the growth rate of the instability is dominated by higher-order terms in the expansion.