Front Curvature Evolution and Hydrodynamics Instabilities
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It is known that hydrodynamic instabilities in turbulent premixed combustion are described by the Michelson-Sivashinsky (MS) equation. A model of the flame front propagation based on the G-equation and on stochastic fluctuations imposed to the mean flame position is considered. By comparing the governing equation of this model and the MS equation, an equation is derived for the front curvature computed in the mean flame position. The evolution in time of the curvature emerges to be driven by the inverse of the dispersion relation and by the nonlinear term of the MS equation.