Capillary Jumps on Deep Water

Abstract

A locally steep surface gradient or ?jump? may be expected on any steady surface current whose strength U decreases horizontally from supercritical (U > cmin) to subcritical (U < cmin), where cmin is the minimum phase velocity of linear capillary-gravity waves. On the downstream side of the jump, the flow is similar to that in a capillary-gravity wave of solitary type. Suitable conditions for a capillary jump can occur on the front face of a steep gravity wave, near the wave crest. The jump may either trap energy in its neighborhood or leak energy down the front face of the wave. In the latter case, it becomes a source of parasitic capillary waves. The conclusions are supported by recent boundary-integral calculations of the deformation of steep surface waves.