Journal of Fluid Mechanics

Non-symmetric gravity waves on water of infinite depth

Juan A.  Zufiria a1
a1 Applied Mathematics Department, California Institute of Technology. Pasadena, CA 91125, USA

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Two different numerical methods are used to demonstrate the existence of and calculate non-symmetric gravity waves on deep water. It is found that they appear via spontaneous symmetry-breaking bifurcations from symmetric waves. The structure of the bifurcation tree is the same as the one found by Zufiria (1987) for waves on water of finite depth using a weakly nonlinear Hamiltonian model. One of the methods is based on the quadratic relations between the Stokes coefficients discovered by Longuet-Higgins (1978a). The other method is a new one based on the Hamiltonian structure of the water-wave problem.

(Published Online April 21 2006)
(Received August 13 1986)