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Singularity Formation In The Geometry Of Perturbed Shocks Of General Mach Number, Wouter Mostert, Dale I. Pullin, Ravi Samtaney, Vincent Wheatley

Mechanical and Aerospace Engineering Faculty Research & Creative Works

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 …