Analytic study on long wave transformation over a seamount with a pit
Analytic study on long wave transformation over a seamount with a pit
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带坑海山长波变换解析研究
DOI：
10.1016/j.oceaneng.2018.02.012
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发表时间：
2018-04
影响因子：
5
通讯作者：
Zhang Yao
中科院分区：
文献类型：
--
作者：
Wang Gang;Fu Danjuan;Zheng Jinhai;Liang Qiuhua;Zhang Yao
本文推导了线性长波在海底地形上散射的解析解。海山是轴对称的，顶部有一个坑。水深由径向方向上的三项函数定义。长波的线性浅水方程用极坐标表示，并通过分离变量法求解。由于地形是轴对称的，解可以写成傅里叶余弦级数。海山上方的波浪采用Frobenius级数展开，外部区域的水面高程采用Fourier-Bessel级数展开，两者在交点处进行匹配，得到最终解。通过调整地形参数，该解可退化为以往的轴对称坑或水下隆起上波浪传播的解析解。
In this paper, an analytic solution is derived for linear long waves scattering over a submarine seamount landform with a pit. The seamount is axisymmetric with a pit on the top. The water depth is defined by a trinomial function in the radial direction. The governing linear shallow water equation for long waves is expressed in the polar coordination, which is solved through separation of variables. As the topography is axisymmetric, solutions can be written as Fourier-cosine series. Waves over the seamount are expressed using Frobenius series expansion, while the water surface elevation in the outer region is expressed as Fourier-Bessel series, and the final solution is obtained by matching them at the conjunction. The solution can be degenerated into the previous analytic solutions for waves propagation over an axisymmetric pit or a submerged hump by adjusting the topography parameters.
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影响因子：
3.7
作者：
M. Longuet-Higgins
通讯作者：
M. Longuet-Higgins
影响因子：
4.4
作者：
T. Jung;K. Suh
通讯作者：
T. Jung;K. Suh
DOI：
10.2307/3614599
发表时间：
1969-05
期刊：
The Mathematical Gazette
影响因子：
--
作者：
J. Walsh;M. R. Spiegel
通讯作者：
J. Walsh;M. R. Spiegel
影响因子：
2.4
作者：
Song‐Ping Zhu;Yinglong J. Zhang
通讯作者：
Song‐Ping Zhu;Yinglong J. Zhang
影响因子：
2.4
作者：
K. Suh;T. Jung;M. Haller
通讯作者：
K. Suh;T. Jung;M. Haller