Low-Frequency Multidimensional Instabilities for Reacting Shock Waves

A. Majda, V. Roytburd

Research output: Contribution to journalArticle

Abstract

This paper presents a weakly nonlinear analysis for one scenario for the development of transversal instabilities in detonation waves in two space dimensions. The theory proposed and developed here is most appropriate for understanding the behavior of regular and chaotically irregular pulsation instabilities that occur in detonation fronts in condensed phases and occasionally in gases. The theory involves low-frequency instabilities and through suitable asymptotics yields a complex Ginzburg-Landau equation that describes simultaneously the evolution of the detonation front and the nonlinear interactions behind this front. The asymptotic theory mimics the familiar theory of nonlinear hydrodynamic instability in outline; however, there are several novel technical aspects in the derivation because the phenomena studied here involve a complex free boundary problem for a system of nonlinear hyperbolic equations with source terms.

Original languageEnglish (US)
Pages (from-to)135-174
Number of pages40
JournalStudies in Applied Mathematics
Volume87
Issue number2
DOIs
StatePublished - Aug 1 1992

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Shock Waves
Shock waves
Low Frequency
Detonation
Hydrodynamic Instability
Nonlinear Instability
Detonation Wave
Nonlinear Hyperbolic Equation
Complex Ginzburg-Landau Equation
Nonlinear Interaction
Free Boundary Problem
Asymptotic Theory
Source Terms
Nonlinear Analysis
Irregular
Nonlinear analysis
Scenarios
Hydrodynamics
Gases

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Low-Frequency Multidimensional Instabilities for Reacting Shock Waves. / Majda, A.; Roytburd, V.

In: Studies in Applied Mathematics, Vol. 87, No. 2, 01.08.1992, p. 135-174.

Research output: Contribution to journalArticle

Majda, A. ; Roytburd, V. / Low-Frequency Multidimensional Instabilities for Reacting Shock Waves. In: Studies in Applied Mathematics. 1992 ; Vol. 87, No. 2. pp. 135-174.
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