Huete Ruiz de Lira, CésarVelikovich, Alexander L.Martínez Ruiz, DanielCalvo Rivera, Andrés2023-01-112023-01-112021-09-29Huete, C., Velikovich, A. L., Martínez-Ruiz, D., & Calvo-Rivera, A. (2021). Stability of expanding accretion shocks for an arbitrary equation of state. Journal of Fluid Mechanics, 927(A35)0022-11201469-7645 (Online)https://hdl.handle.net/10016/36255We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of hc < h < 1 + 2M2, where h is the D’yakov-Kontorovich parameter, hc is its critical value corresponding to the onset of the instability and M2 is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter h increases from hc to 1 + 2M2, the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range hc < h < 1 + 2M2. Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.40eng© The Author(s), 2021. Published by Cambridge University PressThis is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.Atribución 3.0 EspañaGas dynamicsShock wavesSupersonic flowresearch articleIngeniería Mecánicahttps://doi.org/10.1017/jfm.2021.781open access140Journal of Fluid Mechanics927AR/0000029645