Nonlinear dynamics of premixed flames: from deterministic stages to stochastic influence

Premixed flame propagation is a rich interface problem. Instabilities and nonlinearities lead to the formation of cusps pointing toward the burnt gas. These cusps, which undergo complex dynamics, enhance the reaction rate by increasing the flame surface. These crests can be interpreted as pole solutions of the Michelson-Sivashinsky equation that evolve according to ordinary differential equations. Thanks to a quasi-bidimensional experimental facility (a Hele-Shaw burner) we evaluate the accuracy of the description of flame dynamics by elementary interaction between cusps. In particular, we address the time for which a direct comparison between experiments and numerical integration is feasible. The sensitivity to initial conditions and noise is discussed. We demonstrate that at any time of evolution, interesting features can be recovered by describing the flame surface evolution as pole dynamics.