NONLINEAR MEAN FIELD-HIGH FREQUENCY WAVE INTERACTIONS IN THE INDUCTION ZONE.

Andrew Majda, Rodolfo R. Rosales

Research output: Contribution to journalArticle

Abstract

Simplified asymptotic equations are derived for nonlinear high-frequency mean field wave interactions in chemically reacting gases during the induction period. Rigorous proofs of both enhanced combustion and explosion occurring at times preceding the homogeneous induction time are developed. Asymptotic equations are derived for both the simpler case of a high frequency simple wave interacting with a mean field, as well as for the general resonant wave interaction of many high frequency waves and the mean field. Generally, there is a nonlinear feedback mechanism between the mean field and the high frequency waves which enhances combustion. The equations derived here include, as extremely special cases in a unified fashion, earlier separate theories of both low frequency and pulsed high frequency wave propagation in the induction zone. In these earlier theories, the nonlinear feedback mechanism is completely absent.

Original languageEnglish (US)
Pages (from-to)1017-1039
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume47
Issue number5
StatePublished - Oct 1987

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Wave Interaction
Mean Field
Proof by induction
Nonlinear feedback
Combustion
Explosion
Wave propagation
Wave Propagation
Explosions
Low Frequency
Gases

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

NONLINEAR MEAN FIELD-HIGH FREQUENCY WAVE INTERACTIONS IN THE INDUCTION ZONE. / Majda, Andrew; Rosales, Rodolfo R.

In: SIAM Journal on Applied Mathematics, Vol. 47, No. 5, 10.1987, p. 1017-1039.

Research output: Contribution to journalArticle

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