Parameterization of nonlinear shallow water waves over sloping bottoms |
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| Institution: | 1. MARUM, Center for Marine Environmental Sciences, Universität Bremen, Germany;2. Department of Earth and Ocean Sciences, University of Waikato, New Zealand;1. Department of Civil, Environmental and Infrastructure Engineering, George Mason University, 4400 University Drive, MS 6C1, Fairfax, VA 22030, USA;2. Department of Civil and Environmental Engineering, Virginia Tech, 750 Drillfield Drive, 221E Patton Hall, Blacksburg, VA 24061, USA;3. Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843-3136, USA;1. Deltares, P.O. Box 177, 2600 MH Delft, The Netherlands;2. Delft University of Technology, Faculty of Civil Engineering and Geosciences, Hydraulic Engineering Section, P.O. Box 5048, 2600 GA Delft, The Netherlands;1. Applied Mathematics, University of Twente, The Netherlands;2. LabMath-Indonesia, Bandung, Indonesia;1. HR Wallingford, Howbery Park, Wallingford, Oxfordshire OX10 8BA, UK;2. Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK;3. School of Engineering, The University of Edinburgh, The King''s Buildings, Edinburgh EH9 3JL, UK;4. School of Marine Science and Engineering, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK |
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| Abstract: | Investigation of the bottom slope effects on the nonlinear transformation of irregular waves, which are generated based on JONSWAP spectra, is carried out in a physical wave flume with three slopes (β = 1/15, 1/30, 1/45). The slope effects on the estimation of representative wave height are examined first. To obtain a better estimation of wave height, the slope effect should be considered when slope is larger than 1/30. The nonlinear parameters (bicoherence, skewness and asymmetry) are estimated by using the wavelet-based bispectrum, and the empirical formulae regarding these nonlinear parameters as a function of the local Ursell number are derived based on the present data measured on each slope. The results indicate that the slopes have a negligible effect on the variations of the skewness. The fitted coefficients of the formulae for the other parameters on slope β = 1/15 are clearly different from the results on the slopes β = 1/30 and 1/45, indicating that slope influence on the parameterization cannot be ignored when β > 1/30. Hence, new formulae considering the slope effect are presented. Furthermore, the empirical formulae for the data in surf zone are recommended. |
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