Dynamics and stability of anomalous Saffman-Taylor fingers

The existence of anomalous Saffman-Taylor fingers when a localized disturbance is applied at their tip has been demonstrated by several recent experiments. We show that they form a well-defined family with strong similarities with crystalline dendrites. They are narrower and more stable than normal fingers, their tip is parabolic, and its radius of curvature ρ is proportional to the capillary length $l_0$. For very large velocities, saturation occurs when ρ becomes of the order of the plate spacing. Using localized disturbance and periodic forcing we characterize the amplification of waves on their lateral fronts and we then discuss some implications for dendritic crystalline growth.