Spontaneous singularity formation in converging cylindrical shock waves

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We develop a nonlinear, Fourier-based analysis of the evolution of a perturbed, converging cylindrical strong shock using the approximate method of geometrical shock dynamics (GSD). This predicts that a singularity in the shock-shape geometry, corresponding to a change in Fourier-coefficient decay from exponential to algebraic, is guaranteed to form prior to the time of shock impact at the origin, for arbitrarily small, finite initial perturbation amplitude. Specifically for an azimuthally periodic Mach-number perturbation on an initially circular shock with integer mode number q and amplitude proportional to ϵ1, a singularity in the shock geometry forms at a mean shock radius Ru,c∼(q2ϵ)-1/b1, where b1(γ)
Original languageEnglish (US)
JournalPhysical Review Fluids
Volume3
Issue number7
DOIs
StatePublished - Jul 23 2018

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