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Wind wave modelling in shallow water: with application to the southern North Sea
Luo, W. (1995). Wind wave modelling in shallow water: with application to the southern North Sea. PhD Thesis. Katholieke Universiteit Leuven. Laboratorium voor Hydraulica: Leuven. ISBN 90-5682-003-6. XXIV, 198 pp.

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Document type: Dissertation

    Energy transfer > Energy dissipation > Wave dissipation > Wave breaking
    Forces (mechanics) > Friction > Bottom friction
    Numerical models
    Prediction > Wave predicting
    Water > Shallow water
    Water waves > Surface water waves > Wind waves
    ANE, Belgium, Belgian Coast [Marine Regions]

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  • Luo, W.

    Increased marine activities, particularly in areas of off-shore exploitation and coastal development, have created an urgent need for improved knowledge of wave conditions in the shallow near-shore regions. In this work, objectives have been made to investigate the effects of bottom friction, depth-induced wave breaking, and tidal motions on the wave evolution in shallow water, and to apply the wave model (WAM Cycle 4) to the Belgian coastal waters. Firstly, the effects of different bottom friction formulations on the energy balance equation were quantitatively investigated for fetch-limited shallow water conditions. It was found that the formulation of the bottom friction dissipation has a quite significant effect on the energy balance at shallower water depths. Among the five original formulations for the bottom friction dissipation investigated (i.e., an empirical expression based on the JONSWAP experiment (Hasselmann et al., 1973), three expressions based on the drag law turbulent friction model (Hasselmann and Collins, 1968; Collins, 1972; Madsen et al., 1988a) and one based on the eddy viscosity friction model (Weber, 1991a), a difference as big as 70% for the total energy was reported for a water depth of 15 m and a wind friction velocity of 0.71 ms¯¹. It is revealed that the whitecapping dissipation is dominant in shallow water. The contribution of bottom friction varies clearly with depth, and also from formulation to formulation. The role of bottom friction dissipation becomes more significant as the water becomes shallower. Secondly, it has been proven mathematically and numerically that in shallow water cases, the scaling ability of the energy growth curves with the air friction velocity is model-dependent. The growth curves from the drag law models with a fixed dissipation coefficient Cƒ, scale with the air friction velocity Ua*. The drag law model with a dynamically changing friction factor, the empirical formulation and eddy viscosity model do not scale with the wind friction velocity Ua*. It is concluded that the shallow water data which are presented in dimensionless form (scaled with the air friction velocity) cannot be used to evaluate different model results. Thirdly, the equivalent bottom friction dissipation coefficients are developed so that all five bottom friction dissipation formulations give almost the same growth curves for the total energy and the peak frequency. The equivalent coefficients for the empirical formulation and the three drag law models were obtained and referred to the bottom roughness height in th eddy viscosity model for three different wind velocities and a nondimen sional water depth of 300. The introduced error for other water depths is estimated to be of the order of 5%. The validity of using equivalent coefficients in real circumstances was tested in the southern North Sea. It is concluded that the use of the empirical JONSWAP formulation with the proper equivalent coefficients is, for many practical operational applications, not only computationally efficient, but should also produce results with the same order of accuracy as the more sophisticated models for the bottom friction dissipation. Finally, wave conditions along the Belgian coast are hindcasted by using the Cycle 4 version of the WAM model for the period from October 1992 to March 1993. The hindcast results have been validated by ERS-l satellite data and buoy data and by the cross comparison with the mu-WAVE model hindcasts. The Cycle 4 version of the WAM model has been extended with inclusion of the depth-limited wave breaking source term and with a choice for the bottom friction dissipation source term, i.e., the empirical JONSWAP formulation, the drag law expression or the eddy viscosity model. The effects of bottom friction, depth-induced wave breaking and tidal surge motion on the wave evolution in the Belgian coastal waters have been assessed quantitatively.

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