By systematically changing the mixture composition of a flame on a Bunsen burner the conical shape of the flame can suddenly be transform into triangular 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 coupled to a heat equation modeling the temperature of the burner rim. Numerical computations of the coupled set of equations exhibit rapidly rotating polyhedral patterns, which show the typical saw-toothed shape of the corrugations of the flame. In contrast to earlier considerations of this problem, where the rotation is explained as a result of mode interactions, we find a primary bifurcation to a rotating state, which may explain the high speeds of revolution. [References: 5]
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