A Calculation of Wrinkled Flames

In an earlier work, Sivashinsky derived a nonlinear integro-differential equation for spontaneous hydrodynamic instability of a plane flame front. The simplified form of that equation which describes a1 steady progressive wave of long period is reconsidered here. It is shown to represent a wrinkled flame front whose slope has a logarithmic singularity at each wrinkle. We have computed the flame profile and its speed of propagation more accurately than done previously by Michelson and Sivashinksy, and find that the increase in propagation speed due to wrinkling is in surprisingly good agreement with recent experimental findings.