A higher-order non-hydrostatic σ model for simulating non-linear refraction–diffraction of water waves |
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Authors: | Chih-Chieh Young Chin H Wu Wen-Cheng Liu Jan-Tai Kuo |
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Institution: | 1. Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan;2. Department Civil and Environmental Engineering, 1269D Engineering Hall, University of Wisconsin, Madison, WI 53706-1691, USA;3. Department of Civil and Disaster Prevention Engineering, National United University, Miao-Li 36003, Taiwan |
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Abstract: | A higher-order non-hydrostatic σ model is developed to simulate non-linear refraction–diffraction of water waves. To capture non-linear (or steep) waves, a 4th-order spatial discretization is utilized to approximate the large horizontal pressure gradient. A higher-order top-layer pressure treatment is further implemented to resolve wave propagation. The model's characteristics including linear wave dispersion and non-linearity are carefully examined. The accuracy of the present model using only two vertical layers is validated by laboratory data and the available results predicted by the non-linear Schrödinger equation, Boussinesq-type equations, the non-linear mild slope equation, and the Laplace equation. Features of harmonic generation as well as the influences of dispersion and non-linearity on wave energy transfer processes are discussed. |
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Keywords: | Non-hydrostatic σ model Refraction&ndash diffraction Dispersion Non-linearity |
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