In the framework of a nonlinear model which incorporales the Landau-Darrieus instability mechanism and curvature effects, we study thin premixed flames subjected to incoming velocity fluctuations of known r.m.s, intensity (∼ µ') and length-scale ( ∼ Lint). Specifically, we numerically integrate a forcedevolution equation of Michelson-Sivashinsky type, with periodic boundary conditions and focus attention on the mean spacing 'erul(t)between front crests. The forcing mimics the one-component, near Lorentzian spectrum of moderate, isotropic turbulence; the phases and turnover times are randomly sampled. Processing the results of many runs suggests that: i) in the long-time limit /(:resl fluctuates around a value Ll;lest which, once ensemble-averaged to give the quantity 1/' only feebly depends on the lateral flame extent (if the latter is large enough); instead, AcreI, mainly scales like the marginally-stable wavelength Aneutral of the linearized. unforced evolution equation.ii) oActnJou' 0 and, if u'/SL is small enough, an approximately logarithmic increase of Acrt.JAncutr' with decreasing u'ISL is obtained.iii) At fixed U'/SL' Acrc.JAneulf.1 only weakly depends on L inl_ apparently in a nonmonotonic way and with a shallow minimum when Lint and Ancu,ul approximately coincide.iv) When u'lSL is large enough, a new regime appears, where the front gets more and more often covered with traveling waves.The results i)-iii) are tentatively interpreted in terms of the influence of wrinkle-stretching on hydrodynamic instability. We propose a scaling law for A cm, in the low u'/SLregime; besides Aneutral' Lint and u', it explicitly includes the density ratio and the shape of the forcing energy-spectrum, and it is compatible with all our numerical findings. even for not-so-small intensities of forcing.