Numerical method of studying nonlinear interactions between long waves and multiple short waves |
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Authors: | Xie Tao Kuang Hai-Lan William Perrie Zou Guang-Hui Nan Cheng-Feng He Chao Shen Tao and Chen Wei |
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Institution: | Bedford Institute of Oceanography, B2Y 4A2, Dartmouth,
NS, Canada; School of Information Engineering, Wuhan
University of
Technology, Wuhan 430070, China |
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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. |
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Keywords: | sea surface nonliear
interaction numerical method |
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