### 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 and 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) |
---|---|

Title of host publication | American Society of Mechanical Engineers, Applied Mechanics Division, AMD |

Publisher | ASME |

Pages | 55 |

Number of pages | 1 |

Volume | 77 |

State | Published - 1986 |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*American Society of Mechanical Engineers, Applied Mechanics Division, AMD*(Vol. 77, pp. 55). ASME.

**NONLINEAR WAVE AMPLIFICATION IN THE INDUCTION ZONE FOR REACTING GASES.** / Majda, A. J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Society of Mechanical Engineers, Applied Mechanics Division, AMD.*vol. 77, ASME, pp. 55.

}

TY - GEN

T1 - NONLINEAR WAVE AMPLIFICATION IN THE INDUCTION ZONE FOR REACTING GASES.

AU - Majda, A. J.

PY - 1986

Y1 - 1986

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 and 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 and 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=0022957560&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022957560&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022957560

VL - 77

SP - 55

BT - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

PB - ASME

ER -