Two-dimensional gravity-capillary solitary waveson 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 the deep water at speeds close to the minimum phase speed c(min) = 23 cm s(-1). Four different states are observed according to the forcing speed. 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 a 2-D local depression 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 three-dimensional 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). They agree with each other very well. In particular, based on a linear stability analysis, we give a theoretical proof for the transverse instability of the 2-D gravity capillary solitary waves on deep water.