Conditions of Instability of a Flame Front in a Weakly Inhomogeneous Flow

The stability of a flame front in a combustible gas mixture flow is investigated. The flame is treated as a gasdynamic discontinuity, the gas is assumed to be dynamically incompressible, and the gravity force is neglected. It is assumed that in the undisturbed state the free-stream velocity component u , tangential to the front, is nonzero and can vary along the front; the normal mixture-velocity component u _n is constant along the front. A criterion distinguishing the absolute and convective instability of a skew flame front on which u =const is formulated. It is shown that the condition of instability of an inhomogeneous front on which the tangential component u (x) varies slowly coincides with the condition of absolute instability of a homogeneous front on which u is constant and equal to the u (x) minimum.