Nonlinear Mean Field-High Frequency Wave Interactions in the Induction Zone

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.