We prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.

%V 240 %P 99 - 202 %8 2021/04/01 %@ 1432-0673 %G eng %U https://doi.org/10.1007/s00205-021-01607-w %N 1 %! Archive for Rational Mechanics and Analysis