On the hydrodynamic stability of curved premixed flames

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Abstract
We propose a non-linear, model equation describing the dynamics of finite amplitude disturbances superimposed to a two-dimensional, weakly unstable, flame tip of parabolic shape. By showing that solutions of this equation admit a pole decomposition, we illustrate how the local curvature effects, non-linearity and the geometry-induced flame stretch compete with the hydrodynamic instability. Cases of stability, of metastability or leading to « sidecusping » are exhibited. For spatially-periodic disturbances, a non-linear analog to Zel'dovich et al.'s criterion (C. S. T. 24 (1980)) is obtained. The appearance of steady tip-splitting is also shown to be non-generic in the class of pole-decomposable solutions

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