Rotating polyhedral flames

By systematically changing the mixture composition of a flame on a Bunsen b urner the conical shape of the flame can suddenly be transform into triangu lar cells forming a polyhedron. Often the polyhedron rotates rapidly about its vertical axis. We present a weakly nonlinear analysis which results in a Kuramoto-Sivashinsky equation describing cellular flames, which is couple d to a heat equation modeling the temperature of the burner rim. Numerical computations of the coupled set of equations exhibit rapidly rotating polyh edral patterns, which show the typical saw-toothed shape of the corrugation s of the flame. In contrast to earlier considerations of this problem, wher e the rotation is explained as a result of mode interactions, we find a pri mary bifurcation to a rotating state, which may explain the high speeds of revolution.