MEAN EVOLUTION OF WRINKLE WAVELENGTHS IN A MODEL OF WEAKLY-TURBULENT PREMIXED FLAME

New informations on weakly-turbulent premixed flames in the cusped-fla me regime are obtained upon studying a Michelson-Sivashinsky equation whose solution (the instantaneous flame shape) is excited by the influ ence of a weak, pseudo-random additive forcing that is meant to mimic incoming velocity fluctuations. Attention is focused on the time-depen dent mean spacing l(c)(t) between crests, in cases where the front is dat before forcing is switched on. Despite the complexity of each indi vidual run, a surprisingly simple history Lambda(c)(t) always emerges upon averaging l(c)(t) over many realizations of the forcing function, especially in the limit of weak forcings: a noise-triggered linear st age is followed by a stage of crest-coalescence during which d Lambda( c)/dt is a constant and the direct role of forcing is minor; then, rat her abruptly, an equilibrium stage is reached where Lambda(c)(t) acqui res a time-independent value because the crest implants induced by the noise statistically equilibrate the coalescences. Improved or new sca ling-laws, including dynamical ones, are suggested numerically and the oretically for each of the aforementioned stages.