COALESCENCE PROBLEMS IN THE THEORY OF EXPANDING WRINKLED PREMIXED FLAMES

In the framework of a Michelson-Sivashinsky (MS) evolution equation fo r the front shape we study cylindrically-expanding premixed flames, fo cusing attention on the spontaneous dynamics of collections of finite- amplitude wrinkles. To begin with, we consider sharp crests described by pole-decomposed solutions to the MS equation, for which the flame d ynamics is reduced to a finite set of Complex ODE's. The latter are si mplified in the limit of large flame radii to result in a restricted N -body problem (with long-range interactions) for the real angular loca tions of the wrinkle crests. The corresponding statistical problem of coalescence/expansion competition is treated approximately, by a mean- held method, and yields analytical predictions for the cell-size distr ibutions vs. time. Comparisons with spectral integrations of the MS eq uation and with a simulation of the restricted N-body problem reveal f air agreements. Next we consider initial conditions outside the previo us class, yet again representing sharp, alike crests; provided a certa in crest ''weight'' is suitably fitted, the above mean-field model sti ll gives fair predictions. However, we also show that small difference s in initial conditions can suddenly induce late implants, at least wh en the mean flame speed is considered constant. Finally, we evoke unso lved problems e.g. difficulties about attributing the recently suggest ed t(3/2) flame size growth to the unfolding of initial conditions and we give hints on how to account for crest implants within a mean-fiel d method.