Cascading Cellular Flames

Source abstract

The problem of a flame stabilized by a line source of fuel of strength $2\pi \kappa$ is solved numerically. As $\kappa$ is varied, first a bifurcation from an axisymmetric solution to a stationary cellular solution is found. Increasing $\kappa$ further, a sequence of transitions to stationary cellular solutions of increasing mode numberis found. Each transition is accompanied by a region of bistability where two stable stationary cellular solutions coexist, each with its own domain of attraction. Evidence is presented to show that the modal transitions occur via subcritical bifurcations.