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  • Journal of Fluid Mechanics, Volume 184
  • November 1987, pp. 183-206

Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth

  • Juan A. Zufiria (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112087002854
  • Published online: 01 April 2006
Abstract

A weakly nonlinear model is developed from the Hamiltonian formulation of water waves, to study the bifurcation structure of gravity-capillary waves on water of finite depth. It is found that, besides a very rich structure of symmetric solutions, non-symmetric Wilton's ripples exist. They appear via a spontaneous symmetrybreaking bifurcation from symmetric solutions. The bifurcation tree is similar to that for gravity waves. The solitary wave with surface tension is studied with the same model close to a critical depth. It is found that the solution is not unique, and that further non-symmetric solitary waves are possible. The bifurcation tree has the same structure as for the case of periodic waves. The possibility of checking these results in low-gravity experiments is postulated.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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