Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems

Numerical solutions for three-dimensional gravity capillary waves in water of finite depth are presented. The full Euler equations are used and the waves are calculated by a boundary integral equation method. The findings generalize previous results of Părău, Vanden-Broeck, and Cooker [J. Fluid Mech. 536, 99 (2005)] in water of infinite depth. It is found that there are both lumps that bifurcate from linear sinusoidal waves and other fully localized solitary waves which exist for large values of the Bond number. These findings are consistent with rigorous analytical results and asymptotic calculations. The relation between the solitary waves and free surface flows generated by moving disturbances is also explored.