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Abstract
New informations on weakly-turbulent premixed flames in the cusped-flame regime are obtained upon studying a Michelson-Sivashinsky equation whose solution (the instantaneous flame shape) is excited by the influence of a weak, pseudo-random additive forcing, that is meant to mimic incoming velocity fluctuations. Attention is focused on the time-dependent mean spacing lc{t) between crests, in cases where the front is flat before forcing is switched on. Despite the complexity of each individual run, a surprisingly simple history Ac(t) always emerges upon averaging lc(t) over many realizations of the forcing function, especially in the limit of weak forcings: a noise-triggered linear stage is followed by a stage of crest-coalescence during which dAJdt is a constant and the direct role of forcing is minor; then, rather abruptly, an equilibrium stage is reached where Ac(t) acquires a time-independent value because the crest implants induced by the noise statistically equilibrate the coalescences. Improved or new scaling-laws, including dynamical ones, are suggested numerically and theoretically for each of the aforementioned stages.
