LARGE-AMPLITUDE STEADY GRAVITY WATER WAVES WITH GENERAL VORTICITY AND CRITICAL LAYERS
We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging, and no assumptions regarding the absence of stagnation points and critical layers are made. Using conformal mappings and a new reformulation of Bernoulli’s equation, we uncover an equivalent formulation as “identi