On a distorted flame front as a hydrodynamic discontinuity

The radius of curvature of a steady distorted flame often turns out to be considerably larger than the width of the thermal structure of the flame. Thus, even under finite deformations of the flame, its structure remains quasi-one-dimensional. This property enables the propagation velocity of a distorted flame front (relative to the gas) to be determined explicitly as a function of the hydrodynamic field and the physico-chemical parameters of the gaseous mixture. With the aid of this relationship one can try to determine the shape of the front in a model which is external with respect to the flame structure and treats the flame as a density jump in an ideal incompressible fluid. As applications, we consider (1) the structure of a Bunsen cone, (2) the extinction of a flame in a divergent flow and (3) the propagation velocity of a corrugated flame.