Analytic description of the evolution of two-dimensional flame surfaces

The passive propagation of wrinkled, non-folding, premixed flames in quiescent and spatially periodic flow fields is investigated by employing the scalar field, G-equation formulation. Rather than solving the G-equation directly, we transform it into a g equation, which is a differential equation governing the evolution of the slope of the flame shape in two-dimensional flows. For the Landau limit of flame propagation with constant flame speed, the resulting g-equation degenerates to a quasi-linear wave equation in a quiescent flow. For the stretch-affected propagation mode in which the flame propagation speed is curvature-dependent, the resulting g-equation is in the general form of the Burgers' equation. Analytical solutions were obtained for several flame and flow types, revealing some interesting characteristics of the geometry and propagation of the flame, including the formation of cusps and their inner structure, and the augmentation of the average burning velocity through flame wrinkling.