  In this paper we prove the existence of water waves with sign-changing Taylor
sign coefficients, that is, the strong Taylor sign holds initially, while
breaks down at a later time, and vice versa. Such a phenomenon can be regarded
as the transition between the stable and unstable regime in the sense of
Rayleigh-Taylor of water waves. As a byproduct, we prove the sharp
wellposedness of 2d water waves in Gevrey-2 spaces.
