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Nonlinear three-dimensional gravity–capillary solitary waves

2005; Cambridge University Press; Volume: 536; Linguagem: Inglês

10.1017/s0022112005005136

1469-7645

Emilian I. Părău, Jean‐Marc Vanden‐Broeck, Mark J. Cooker,

Navier-Stokes equation solutions

Steady three-dimensional fully nonlinear gravity–capillary solitary waves are calculated numerically in infinite depth. These waves have decaying oscillations in the direction of propagation and monotone decay perpendicular to the direction of propagation. They travel at a velocity of linear gravity–capillary waves. It is shown that the structure of the solutions in three dimensions is similar to that found by Vanden-Broeck & Dias (J. Fluid Mech. vol. 240, 1992, pp. 549–557) for the corresponding two-dimensional problem.