Analytical Interaction of the Acoustic Wave and Turbulent Flame

A modified resonance model of a weakly turbulent flame in a high-frequency acoustic wave is derived analytically. Under the mechanism of Darrieus--Landau instability, the amplitude of flame wrinkles, which is as functions of the expansion coefficient and the perturbation wave number, increases greatly independent of the `stationary' turbulence. The high perturbation wave number makes the resonance easier to be triggered but weakened with respect to the extra acoustic wave. In a closed burning chamber with the acoustic wave induced by the flame itself, the high perturbation wave number is to restrain the resonance for a realistic flame.