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Analytic study on long wave transformation over a seamount with a pit

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journal contribution
posted on 14.01.2019, 11:53 by Gang Wang, Danjuan Fu, Jinhai Zheng, Qiuhua LiangQiuhua Liang, Yao Zhang
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.

Funding

The presented research was supported by the National Natural Science Foundation of China (NO.: 51579090), the National Science Fund for Distinguished Young Scholars (NO.: 51425901) and Innovation Project of Colleges and Universities in JiangSu Province (NO.: 2015B41814).

History

School

  • Architecture, Building and Civil Engineering

Published in

Ocean Engineering

Volume

154

Pages

167 - 176

Citation

WANG, G. ... et al, 2018. Analytic study on long wave transformation over a seamount with a pit. Ocean Engineering, 154, pp.167-176.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

04/02/2018

Publication date

2018-02-16

Notes

This paper was accepted for publication in the journal Ocean Engineering and the definitive published version is available at https://doi.org/10.1016/j.oceaneng.2018.02.012

ISSN

0029-8018

Language

en