Local stability of a fluid interface near a zero-vorticity point

There are many examples of fluid interfaces which give rise to small-scale structures in uniform or nearly uniform flows: ``skirted'' bubbles, filaments trailing rising drops and bubbles or forming at the tip of coaxial jets and others. It is argued that these phenomena are due to a peculiar instability in the neighborhood of a zero-vorticity point (or line). A local stability analysis supports this conjecture and is further illustrated by some numerical results.