Instability of flow over a supersonic ramp

We consider high Reynolds number flow over a compression ramp with length scales of the classical triple-deck structure. Previous studies of the stability have focused on initial-value problems, showing growth of short-wavelength and high-frequency disturbances. To date, no physical or numerical origin has been robustly identified (see [1-4]) for this behaviour. Contrary to previous results, we show that steady compression-ramp solutions can be weakly inflectional even at moderate ramp angles and that the growing disturbances are a physical (not numerical) instability of the triple-deck equations. These modes are not directly connected to the eigenrelation derived in [5] for long-wave Rayleigh instability despite the presence of an inflection point in the flow. Both the spatial and temporal instability problems are investigated for large but finite frequencies and wavenumbers respectively, and in the spatial problem the growth is shown to correspond to a local eigenvalue problem.

[1] Cassel, K., et al (1995), J. Fluid Mech. 300, 265–286.

[2] Fletcher, A. J. P., et al (2004), J. Fluid Mech. 517, 309–330.

[3] Logue, R. P., et al (2014), Phil. Trans. R. Soc. A 372.

[4] Exposito, D., et al (2021), J. Fluid Mech. 922.

[5] Tutty, O. R. & Cowley, S. J. (1986) J. Fluid. Mech. 168, 431-456.