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Interactions of waves with a body floating in an open water channel confined by two semi-infinite ice sheets

Published online by Cambridge University Press:  23 April 2021

Zhi Fu Li Open the ORCID record for Zhi Fu Li [Opens in a new window] ,
Guo Xiong Wu Open the ORCID record for Guo Xiong Wu [Opens in a new window]  and
Kang Ren Open the ORCID record for Kang Ren [Opens in a new window]
Zhi Fu Li
Affiliation:
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang212003, PR China
Guo Xiong Wu*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 7JE, UK
Kang Ren
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 7JE, UK
*
†Email address for correspondence: [email protected]
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Abstract

Wave radiation and diffraction problems of a body floating in an open water channel confined by two semi-infinite ice sheets are considered. The linearized velocity potential theory is used for fluid flow and a thin elastic plate model is adopted for the ice sheet. The Green function, which satisfies all the boundary conditions apart from that on the body surface, is first derived. This is obtained through applying Fourier transform in the longitudinal direction of the channel, and matched eigenfunction expansions in the transverse plane. With the help of the derived Green function, the boundary integral equation of the potential is derived and it is shown that the integrations over all other boundaries, including the bottom of the fluid, free surface, ice sheet, ice edge as well as far field will be zero, and only the body surface has to be retained. This allows the problem to be solved through discretization of the body surface only. Detailed results for hydrodynamic forces are provided, which are generally highly oscillatory owing to complex wave–body–channel interaction and body–body interaction. In depth investigations are made for the waves confined in a channel, which does not decay at infinity. Through this, a detailed analysis is presented on how the wave generated by a body will affect the other bodies even when they are far apart.

JFM classification

Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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