New families of steep solitary waves in water of finite depth with constant vorticity

摘要

Solitary waves with constant vorticity in water of finite depth are considered. Previous calculations showed that there are branches of solutions characterized by a limiting configuration with a 120° angle at the crest of the wave and others which ultimately approach closed regions of constant vorticity in contact with the bottom of the channel. Here it is shown that there are additional families of solutions. As the acceleration of gravity approaches zero, these new solutions approach configurations consisting of a wave with an arbitrary number of circular regions of fluid in rigid body rotation on top of its crest.