An equation of surface dynamics modeling flame fronts as density discontinuities in potential flows

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Abstract
A coordinate‐free equation modeling the flame front dynamics as propagation of density discontinuity within the framework of the Darreus–Landau hydrodynamical model is derived under the assumption of potential flow. The assumption is based on the observation that for slightly perturbed plane configurations the flow is irrotational if the thermal expansion of the gas is weak. A relationship with an equation obtained earlier for a slightly perturbed plane flame front is established in the case of weak thermal expansion. An invariant equation simultaneously modeling the thermal‐diffusional and the hydrodynamical instabilities is suggested, which also can be reduced to earlier results in appropriate limits.