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Low‐Frequency Multidimensional Instabilities for Reacting Shock Waves
Author(s) -
Majda A.,
Roytburd V.
Publication year - 1992
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1992872135
Subject(s) - detonation , nonlinear system , instability , shock front , shock wave , physics , classical mechanics , space (punctuation) , shock (circulatory) , boundary value problem , mechanics , boundary (topology) , mathematical analysis , mathematics , explosive material , quantum mechanics , computer science , medicine , chemistry , organic chemistry , operating system
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.