*Vera Hur, Department of Mathematics, University of Illinois*

**Stokes waves in a constant vorticity flow: theory and numerics**

Stokes in the 1800s made many contributions about periodic waves at the surface of water, under the influence of gravity, propagating in permanent form a long distance at a practically constant velocity. In an irrotational flow, for instance, he observed that crests become sharper and troughs flatter as the amplitude increases, and that the so-called wave of greatest height, or extreme wave, possesses a 120 degree's angle at the crest. The irrotational flow assumption is justified in many situations, and facilitates rigorous analysis and numerical computation. However, rotational effects are significant in many others. I will review recent progress in a constant vorticity flow. Numerical findings include folds and gaps in the wave speed vs. amplitude plane, and a profile enclosing multiple bubbles of fluids. I will discuss analytical and numerical applications if time permits.