### 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 language | English (US) |
---|---|

Pages (from-to) | 1017-1039 |

Number of pages | 23 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 47 |

Issue number | 5 |

State | Published - Oct 1987 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*47*(5), 1017-1039.

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

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 47, no. 5, pp. 1017-1039.

}

TY - JOUR

T1 - NONLINEAR MEAN FIELD-HIGH FREQUENCY WAVE INTERACTIONS IN THE INDUCTION ZONE.

AU - Majda, Andrew

AU - Rosales, Rodolfo R.

PY - 1987/10

Y1 - 1987/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023430475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023430475&partnerID=8YFLogxK

M3 - Article

VL - 47

SP - 1017

EP - 1039

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -