Two-dimensional gravity--capillary solitary waves on deep water: Generation and transverse instability.

Two-dimensional (2-D) gravity--capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of deep water with speeds close to the minimum phase speed $c_{\min } =$23$\mbox{cm/s}$. Four different states are observed according to forcing speeds. At relatively low speeds below $c_{\min } $, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{\min } $, nonlinear 2-D gravity--capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{\min } $, periodic shedding of local depressions is observed behind the moving forcing. Finally, at relatively high speeds above $c_{\min } $, a pair of short and long linear waves is observed, respectively, ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity--capillary solitary waves and, further, the resultant formation of 3-D gravity--capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity--capillary solitary wave solutions near $c_{\min } $and they agree with each other very well.