On the stability of piston-driven planar shocks

dc.contributor.authorCalvo Rivera, Andrés
dc.contributor.authorVelikovich, Alexander L.
dc.contributor.authorHuete Ruiz de Lira, César
dc.contributor.funderComunidad de Madrides
dc.contributor.funderUniversidad Carlos III de Madrides
dc.contributor.funderAgencia Estatal de Investigación (España)es
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.description.abstractWe 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.en
dc.description.sponsorshipThe work of A.C.R and C.H. has been supported with project TED2021-129446B-C41 (MICINN/FEDER, UE). The work of C.H. has also received support from the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M (H2SAFE-CM-UC3M). The work of A.L.V. has been supported by the National Nuclear Security Administration of the US Department of Energy.en
dc.identifier.bibliographicCitationCalvo-Rivera, A., Velikovich, A. L., & Huete, C. (2023). On the stability of piston-driven planar shocks. Journal of Fluid Mechanics, 964(A33)en
dc.identifier.publicationtitleJournal of Fluid Mechanicsen
dc.publisherCambridge University Pressen
dc.relation.projectIDComunidad de Madrid. H2SAFE-CM-UC3Mes
dc.relation.projectIDGobierno de España. TED2021-129446B-C41es
dc.rights© The Author(s), 2023. Published by Cambridge University Press.en
dc.rightsThis is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.subject.ecienciaIngeniería Industriales
dc.subject.otherGas dynamicsen
dc.subject.otherShock wavesen
dc.titleOn the stability of piston-driven planar shocksen
dc.typeresearch article*
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