The characteristics method and cusped flame fronts

The kinematic effects of a space-time forced velocity held upon a thin premixed flame, stabilized above a circular cross-section burner, are studied in order to point out the non-linearities due to a sufficiently high velocity perturbation level whose RMS amplitudes remain nonetheless inferior to the normal burning velocity. The present calculation proposes to seek a solution using the characteristics method, without any linearized calculation, to express these effects. A front evolution equation is interpreted as the differentiated form of a conservation equation of the radial distance between two points of the front. These modelling results are used to interpret experiments of a vibrating flame subjected to a space-time sinusoidal velocity held. In this last case, the limit of cusps formation is represented as a similarity law expressing the nondimensional perturbation amplitude versus a Strouhal number of the aero-acoustic reactive medium.