Interaction of Pulsating and Spinning Waves in Condensed Phase Combustion

We employ a nonlinear stability analysis in the neighborhood of a multiple bifurcation point to describe the interaction of pulsating and spinning modes of condensed phase combustion. Such phenomena occur in the synthesis of refractory materials. In particular, we consider the propagation of combustion waves in a long thermally insulated cylindrical sample and show that steady, planar combustion is stable for a modified activation energy/melting parameter less than a critical value. Above this critical value primary bifurcation states, corresponding to time-periodic pulsating and spinning modes of combustion, emanate from the steadily propagating solution. By varying the sample radius, we split a multiple bifurcation point to obtain bifurcation diagrams which exhibit secondary, tertiary, and quaternary branching to various types of quasi-periodic combustion waves.