Periodic waves with constant vorticity in water of infinite depth

Periodic waves propagating at a constant velocity at the surface of a fluid with constant vorticity in water of infinite depth are considered. The problem is solved numerically by a boundary-integral-equation method. Simmen & Saffman (Stud. Appl. Maths75, 35, 1985) showed that there are families of solutions which have limiting configurations with a 120° angle at their crests or a trapped bubble at their troughs. It is shown that there are additional families of solutions. These families have limiting configurations with trapped bubbles at their crests. Each bubble is circular and contains fluid in rigid-body rotation. The results are consistent with previous calculations for solitary waves in water of finite depth.