Singularity Formation in the Geometry of Perturbed Shocks of General Mach Number

W. Mostert, D. I. Pullin, Ravi Samtaney, V. Wheatley

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

While planar shock waves are known to be stable to small perturbations in the sense that the perturbation amplitude decays over time, it has also been suggested that plane propagating shocks can develop singularities in some derivative of their geometry (Whitham (1974) Linear and nonlinear waves. Wiley, New York) in a nonlinear, wave reinforcement process. We present a spectral-based analysis of the equations of geometrical shock dynamics that predicts the time to singularity formation in the profile of an initially perturbed planar shock for general shock Mach number. We find that following an initially sinusoidal perturbation, the shock shape remains analytic only up to a finite, critical time that is a monotonically decreasing function of the initial perturbation amplitude. At the critical time, the shock profile ceases to be analytic, corresponding physically to the incipient formation of a “shock-shock” or triple point. We present results for gas-dynamic shocks and discuss the potential for extension to shock dynamics of fast MHD shocks.
Original languageEnglish (US)
Title of host publication31st International Symposium on Shock Waves 1
PublisherSpringer International Publishing
Pages887-894
Number of pages8
ISBN (Print)9783319910192
DOIs
StatePublished - Mar 22 2019

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