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Hydroelastic interaction between water waves and an array of circular floating porous elastic plates

Published online by Cambridge University Press:  06 August 2020

Siming Zheng Open the ORCID record for Siming Zheng [Opens in a new window] ,
Michael H. Meylan Open the ORCID record for Michael H. Meylan [Opens in a new window] ,
Guixun Zhu ,
Deborah Greaves  and
Gregorio Iglesias
Siming Zheng*
Affiliation:
School of Engineering, Computing and Mathematics, University of Plymouth, Drake Circus, PlymouthPL4 8AA, UK
Michael H. Meylan
Affiliation:
School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan2308, Australia
Guixun Zhu
Affiliation:
School of Engineering, Computing and Mathematics, University of Plymouth, Drake Circus, PlymouthPL4 8AA, UK
Deborah Greaves
Affiliation:
School of Engineering, Computing and Mathematics, University of Plymouth, Drake Circus, PlymouthPL4 8AA, UK
Gregorio Iglesias
Affiliation:
School of Engineering, Computing and Mathematics, University of Plymouth, Drake Circus, PlymouthPL4 8AA, UK MaREI, Environmental Research Institute and School of Engineering, University College Cork, Cork P43 C573, Ireland
*
†Email address for correspondence: siming.zheng@plymouth.ac.uk
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Abstract

A theoretical model based on linear potential flow theory and an eigenfunction matching method is developed to analyse the hydroelastic interaction between water waves and multiple circular floating porous elastic plates. The water domain is divided into the interior and exterior regions, representing the domain beneath each plate and the rest, which extends towards infinity horizontally, respectively. Spatial potentials in these two regions can be expressed as a series expansion of eigenfunctions. Three different types of edge conditions are considered. The unknown coefficients in the potential expressions can be determined by satisfying the continuity conditions for pressure and velocity at the interface of the two regions, together with the requirements for the motion/force at the edge of the plates. Apart from the straightforward method to evaluate the exact power dissipated by the array of porous elastic plates, an indirect method based on Green's theorem is determined. The indirect method expresses the wave-power dissipation in terms of Kochin functions. It is found that wave-power dissipation of an array of circular porous elastic plates can be enhanced by the constructive hydrodynamic interaction between the plates, and there is a profound potential of porous elastic plates for wave-power extraction. The results can be applied to a range of floating structures but have special application in modelling energy loss in flexible ice floes and wave-power extraction by flexible plate wave-energy converters.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A20
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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