Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 465, Issue 2110, Pages 3083-3102Publisher
ROYAL SOC
DOI: 10.1098/rspa.2009.0224
Keywords
Gaussian; wave group; freak wave; nonlinear Schrodinger equation
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Funding
- EPSRC
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This paper sets out an approximate analytical model describing the nonlinear evolution of a Gaussian wave group in deep water. The model is derived using the conserved quantities of the cubic nonlinear Schrodinger equation (NLSE). The key parameter for describing the evolution is the amplitude-to-wavenumber bandwidth ratio, a quantity analogous to the Benjamin-Feir index for random sea-states. For smaller values of this parameter, the group is wholly dispersive, whereas for more nonlinear cases, solitons are formed. Our model predicts the characteristics and the evolution of the groups in both regimes. These predictions are found to be in good agreement with numerical simulations using the NLSE and are in qualitative agreement with numerical results from a fully nonlinear potential flow solver and experimental results.
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