Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations

An asymptotic nonlinear integrodifferential equation is derived for spontaneous instability of the plane front of a laminar flame. If the combustible mixture is deficient in the light component, spontaneous instability will lead to self-turbulization of the flame, and the flame front assumes a strongly nonstationary cellular structure. If there is an excess of the light component, spontaneous instability produces stationary, irregular wrinkles on the flame front, and the flame continues to propagate in a laminar regime. It is shown that in all cases spontaneous instability of the flame implies an increase in its propagation velocity.