  Propagation of turbulent premixed flames influenced by the intrinsic hydrodynamic flame instability (the Darrieus-Landau instability) is considered in a two-dimensional case using the model nonlinear equation proposed recently. The nonlinear equation takes into account both influence of external turbulence and intrinsic properties of a flame front, such as small but finite flame thickness and realistically large density variations across the flame front. Dependence of the flame velocity on the turbulent length scale, on the turbulent intensity and on the density variations is investigated in the case of weak non-linearity and weak external turbulence. It is shown that the Darrieus-Landau instability influences the flamelet velocity considerably. The obtained results are in agreement with experimental data on turbulent burning of moderate values of the Reynolds number. 
Effect of the Darrieus-Landau instability on turbulent flame velocity