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Numerical method of studying nonlinear interactions between long waves and multiple short waves
Authors:Xie Tao  Kuang Hai-Lan  William Perrie  Zou Guang-Hui  Nan Cheng-Feng  He Chao  Shen Tao and Chen Wei
Institution:Bedford Institute of Oceanography, B2Y 4A2, Dartmouth, NS, Canada; School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China
Abstract:Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.
Keywords:sea surface  nonliear interaction  numerical method
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