The Role of Non-Hydrostatic Effects in Nonlinear Dispersive Wave Modeling (original) (raw)
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With the objective of modeling coastal wave dynamics taking into account nonlinear and dispersive effects, a highly accurate nonlinear potential flow model was developed. The model is based on the time evolution of two surface quantities: the free surface position and the free surface velocity potential. A spectral approach is used to resolve vertically the velocity potential in the domain, by decomposing the potential using an orthogonal basis of Chebyshev polynomials. With this approach, a wide range of relative water depths can be simulated, as demonstrated here with the propagation of nonlinear regular waves over a flat bottom with kh = 2π and 4π (where k is the wave number and h the water depth). The model is then validated by comparing the simulation results to experimental data for four non-breaking wave test cases: (1) nonlinear dynamics of a wave train generated by a piston-type wavemaker in constant water depth, (2) shoaling of a regular wave train on beach with constant slope up to the breaking point, (3) propagation of regular waves over a submerged bar, and (4) propagation of nonlinear irregular waves over a barred beach. The test cases show the ability of the model to
Journal of Computational Physics, 2007
A fully nonlinear and fully dispersive method for the interaction between free surface waves and a variable bottom topography in space and time in three dimensions is derived. A Green function potential formulation expresses the normal velocity of the free surface in terms of the bathymetry and its motion. An explicit, fast version of the method is derived in Fourier space with evaluations using FFT. Practice shows that the explicit method captures the most essential parts of the wave field. This leads to a time-integration that is very accurate and orders of magnitude faster than existing full potential formulation methods. Fully resolved simulations of the nonlinear and dispersive wave fields are enabled from the generation to the shoaling of the waves, including the onshore flow which is handled by suitable numerical beaches.