Modeling nonlinear wave–wave interactions with the elliptic mild slope equation |
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| Institution: | 1. Department of Maritime Systems Engineering, Texas A&M University at Galveston, Galveston, TX 77553, United States;2. Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, United States;1. Department of Petroleum Engineering, China University of Petroleum (East China), 266580 Qingdao, China;2. Chongqing University of Science and Technology, 401331 Chongqing, China;1. Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;2. Norwegian Marine Technology Research Institute (MARINTEK), NO-7450 Trondheim, Norway |
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| Abstract: | An approach is developed to simulate wave–wave interactions using nonlinear elliptic mild-slope equation in domains where wave reflection, refraction, diffraction and breaking effects must also be considered. This involves the construction of an efficient solution procedure including effective boundary treatment, modification of the nonlinear equation to resolve convergence issues, and validation of the overall approach. For solving the second-order boundary-value problem, the Alternating Direction Implicit (ADI) scheme is employed, and the use of approximate boundary conditions is supplemented, for improved accuracy, with internal wave generation method and dissipative sponge layers. The performance of the nonlinear model is investigated for a range of practical wave conditions involving reflection, diffraction and shoaling in the presence of nonlinear wave–wave interactions. In addition, the transformation of a wave spectrum due to nonlinear shoaling and breaking, and nonlinear resonance inside a rectangular harbor are simulated. Numerical calculations are compared with the results from other relevant nonlinear models and experimental data available in literature. Results show that the approach developed here performs reasonably well, and has thus improved the applicability of this class of wave transformation models. |
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| Keywords: | Nonlinear mild-slope equation Wave–wave interactions Nonlinear harbor resonance |
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