PMID: 15244938Jul 13, 2004Paper

Initial-value-problem solution for isolated rippled shock fronts in arbitrary fluid media

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Jason W Bates

Abstract

Following the work of Roberts [Los Alamos Scientific Laboratory Report No. LA-299, 1945 (unpublished)], we investigate the effect of small two-dimensional perturbations on an isolated, planar shock front moving steadily through an inviscid fluid medium with an arbitrary equation of state (EOS). In the context of an initial-value problem, we derive explicit analytical expressions for the linearized, time-dependent Fourier coefficients associated with an initial corrugation of the front. The temporal evolution of these coefficients superficially resembles the attenuated "ringing" of a damped harmonic oscillator, but with the important distinctions that the frequency of oscillation is not constant, and that the damping factor is not simply an exponential function of time t. It is shown that at least two three-parameter families of stable solutions exist, one more strongly damped than the other. In both cases, we find that the envelope of oscillations decays asymptotically as t(-3/2), with shorter wavelengths dying out earlier than longer ones. For a particular perturbed-shock system, the strength of the front and the EOS properties of the material through which it propagates determine the applicable family of solutions. Theoretica...Continue Reading

References

Oct 4, 2000·Physical Review Letters·J W Bates, D C Montgomery
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J O KaneA Calder
Apr 19, 1991·Science·C F McKee, B T Draine

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Citations

Apr 8, 2010·The Review of Scientific Instruments·P M CelliersG W Collins
Jan 18, 2007·The Journal of the Acoustical Society of America·B Edward McDonald
Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J W Bates
May 27, 2017·Physical Review Letters·S OpieR P Johnson
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J G Wouchuk, J López Cavada

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