Darrieus-Landau instabilities in the framework of the G-equation
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We consider a model formulation of the flame front propagation in turbulent premixed combustion based on stochastic fluctuations imposed to the mean flame position. In particular, the mean flame motion is described by a G-equation, while the fluctuations are described according to a probability density function which characterizes the underlying stochastic motion of the front. The proposed approach reproduces as special cases the G-equation along the motion of the mean flame position, when the stochastic fluctuations are removed, and the Zimont & Lipatnikov model, when a Gaussian density for fluctuations is used together with the assumption of a plane front. The potentiality of the approach is here investigated further focusing on the Darrieus-Landau (hydrodynamic) instabilities. In particular, this model formulation is set to lead to the Michelson-Sivashinsky equation. Furthermore, a formula that connects the consumption speed and the front curvature is established.