Fully dispersive dynamic models for surface water waves above varying bottom, Part 2: Hybrid spatial-spectral implementations

Embrecht W.C. van Groesen, I. van der Kroon

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    In Part 1 (van Groesen and Andonowati [1]), we derived models for the propagation of coastal waves from deep parts in the ocean to shallow parts near the coast. In this paper, we will describe hybrid spatial-spectral implementations of the models that retain the basic variational formulation of irrotational surface waves that underlays the derivation of the continuous models. It will be shown that the numerical codes are robust and efficient from results of simulations of two test cases of waves above a 1:20 sloping bottom from 30 m to 15 m depth: one simulation of a bichromatic wave train, and one of irregular waves of JONSWAP type. Measurements of scaled experiments at MARIN hydrodynamic laboratory and simulations with two other numerical codes will be used to test the performance. At the end of the full time trace of 3.5 h details of the irregular waves that travelled over more than 5000 m are clearly resolved with a correlation of more than 90%, in calculation times of less than 5% of the physical time. Also freak-like waves that appear in the irregular wave are shown to be modelled to a high degree of accuracy.
    Original languageUndefined
    Pages (from-to)198-211
    Number of pages15
    JournalWave motion
    Issue number1
    Publication statusPublished - Jan 2012


    • EWI-20990
    • Coastal waves
    • Hybrid spatial-spectral implementation
    • Freak waves
    • AB-equation
    • Variational modelling
    • METIS-284926
    • IR-78968
    • Sloping bottom

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