Instability of isolated planar shock waves

Abstract

Previously, expressions governing the temporal evolution of linear perturbations to an isolated, planar, two-dimensional shock front in an inviscid fluid medium with an arbitrary equation of state were derived using a methodology based on Riemann invariants and Laplace transforms [J.W. Bates, Phys. Rev. E 69, 056313 "2004"]. An overlooked yet immediate consequence of this theory is that the stability limits of shocks can be readily determined from a inspection of the poles of the transformed ripple amplitude. Here, it is shown that two classes of instabilities exist for isolated planar shock waves: one in which perturbations grow exponentially in time, and the other in which disturbances are stationary. These results agree with those derived by D'yakov and Kontorovich "by more arduous and somewhat ambiguous means", and serve as an important addendum to our earlier analysis.

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Document Details

Document Type
Technical Report
Publication Date
Jun 07, 2007
Accession Number
ADA480805

Entities

People

  • Jason W. Bates

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Acoustic Waves
  • Amplitude
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Fluid Dynamics
  • Fluid Flow
  • Numerical Analysis
  • Partial Differential Equations
  • Perturbations
  • Phase Transformations
  • Real Variables
  • Shock Waves
  • Two Dimensional
  • Volterra Equations
  • Waves

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.
  • Plasma Physics / Magnetohydrodynamics