LENGTH-SCALES OF WRINKLING OF WEAKLY-FORCED, UNSTABLED PREMIXED FLAMES

In the framework of a nonlinear model which incorporates the Landau-Da rrieus instability mechanism and curvature effects, we study thin prem ixed flames subjected to incoming velocity fluctuations of known r.m.s . intensity (approximately u') and length-scale (approximately L(int)) . Specifically, we numerically integrate a forced evolution equation o f Michelson-Sivashinsky type, with periodic boundary conditions and fo cus attention on the mean spacing l(crest)(t) between front crests. Th e forcing mimics the one-component, near Lorentzian spectrum of modera te, isotropic turbulence; the phases and turnover times are randomly s ampled. Processing the results of many runs suggests that: i) in the l ong-time limit l(crest) fluctuates around a value L(crest) which, once ensemble-averaged to give the quantity LAMBDA(crest), only feebly dep ends on the lateral flame extent (if the latter is large enough); inst ead, LAMBDA(crest) mainly scales like the marginally-stable wavelength LAMBDA(neutral) of the linearized, unforced evolution equation. ii) r tial-derivativeLAMBDA(crest)/partial-derivativeu' < 0 and, if u'/S(L) is small enough, an approximately logarithmic increase of LAMBDA(crest )/LAMBDA(neutral) with decreasing u'/S(L) is obtained. iii) At fixed u '/S(L), LAMBDA(crest)/LAMBDA(neutral) only weakly depends on L(int), a pparently in a nonmonotonic way and with a shallow minimum when L(int) and LAMBDA(neutral) approximately coincide. iv) When u'/S(L) is large enough, a new regime appears, where the front gets more and more ofte n covered with traveling waves. The results i)-iii) are tentatively in terpreted in terms of the influence of wrinkle-stretching on hydrodyna mic instability. We propose a scaling law for LAMBDA(crest) in the low u'/S(L) regime; besides LAMBDA(neutral), L(int) and u', it explicitly includes the density ratio and the shape of the forcing energy-spectr um, and it is compatible with all our numerical findings, even for not -so-small intensities of forcing.