(7)Scattering of water waves by a wave energy device consisting of a pair of co-axial cylinders in a uniform water having finite channel width

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P. Borah, M. Hassan^∗ 

Department of Mathematics, North Eastern Regional Institute of Science and Technology, Itanagar, Arunachal Pradesh 791109, India 

Received 16 February 2020; received in revised form 12 January 2021; accepted 30 January 2021 

Available online 4 February 2021

Abstract

    We consider a device which consists of a floating structure over a cylindrical plate placed at a finite height from the impermeable ocean floor. This paper developes the interaction of linear water waves with such a device. The whole fluid domain is divided into a number of sub-domains and boundary value problems are formulated for each identified sub-domain. The channel multipoles, separation of variables and matched eigenfunction expansion methods allow us to solve boundary value problems for the diffracted velocity potentials in each subdomain. We investigate the wave forces exerted on the proposed device. Consequently, the effects of the various parameters, e.g., drafts, radii, the gap between the cylinders and mainly channel width of the device on the wave forces exerted by the cylinders are presented graphically. We observe a small oscillation nature near the peak value of the exciting force for the particular value of channel width w = 2.4m. The peak value of the exciting forces occurs near the wavenumber kr1 = 1.0 for different width of the channel walls. The obtained results are compared with some available results, and it shows a good agreement between the obtained and available results. 

© 2021 Shanghai Jiaotong University. Published by Elsevier B.V. 

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/)

Keywords: Water waves; Exciting force; Channel multipoles; Channel width; Wavenumber, 2000 MSC 76B07; 76B15.