Abstract
The irrotational Green–Naghdi model for nonlinear wave propagation in deep water is developed to simulate the irregular sea surface of a given directional wave spectrum. The model is derived from Hamilton's principle with a depthwise approximation to the flow field. The nonlinear boundary conditions are exactly satisfied on the actual free surface, and the continuity equation is satisfied exactly within the fluid domain. The ‘level’ of approximation in the depthwise direction is optimally chosen to simulate a given wave spectrum accurately with minimum computational effort. Several numerical techniques also are introduced to cut the computational cost further. Numerical results for two-dimensional nonlinear waves are presented.
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