On the stability of piston-driven planar shocks

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Cambridge University Press
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We present a theoretical and numerical stability analysis for a piston-driven planar shock against two-dimensional perturbations. The results agree with the well-established theory for isolated planar shocks: in the range of hc < h < 1 + 2M2, where h is the Dyakov-Kontorovich (DK) parameter related to the slope of the Rankine-Hugoniot curve, hc is its critical value corresponding to the onset of the spontaneous acoustic emission (SAE) and M2 is the downstream Mach number, non-decaying oscillations of shock-front ripples occur. The effect of the piston is manifested in the presence of additional frequencies occurring by the reflection of the sonic waves on the piston surface that can reach the shock. An unstable behaviour of the shock perturbation is found to be possible when there is an external excitation source affecting the shock, whose frequency coincides with the self-induced oscillation frequency in the SAE regime, thereby being limited to the range hc < h < 1 + 2M2. An unstable evolution of the shock is also observed for planar shocks restricted to one-dimensional perturbations within the range 1 < h < 1 + 2M2. Both numerical integration of the Euler equations via the method of characteristics and theoretical analysis via Laplace transform are employed to cross-validate the results.
Gas dynamics, Shock waves
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Calvo-Rivera, A., Velikovich, A. L., & Huete, C. (2023). On the stability of piston-driven planar shocks. Journal of Fluid Mechanics, 964(A33)