  We prove the existence of small amplitude time quasi-periodic solutions of
the pure gravity water waves equations with constant vorticity, for a
bidimensional fluid over a flat bottom delimited by a space periodic free
interface. Using a Nash-Moser implicit function iterative scheme we construct
traveling nonlinear waves which pass through each other slightly deforming and
retaining forever a quasiperiodic structure. These solutions exist for any
fixed value of depth and gravity and restricting the vorticity parameter to a
Borel set of asymptotically full Lebesgue measure.

Analysis of PDEs