The Stability of Curved Fronts

We investigate some stability properties of different curved fronts, such as the Davies-Taylor bubble and the needle crystal, by analogy with the flame problem studied previously by Zel'dovich et al. Some useful insights on the limitation of the WKB analysis are first presented by using as an example the Saffman-Taylor finger recently considered by Bensimon et al. The analysis of these different fronts shows that, as a general rule, the stability criterion relates nondimensional numbers (characterizing the steady-state solutions) to the amplitude of the initial perturbation at the tip.