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The motion of a freely floating cylinder in the presence of a wall and the approximation of resonances

Published online by Cambridge University Press:  19 April 2016

P. McIver  and
R. Porter
P. McIver*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
R. Porter
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
*
†Email address for correspondence: p.mciver@lboro.ac.uk
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Abstract

A linear theory, based on wide-spacing and high-frequency approximations, is developed to describe resonant behaviour in two-dimensional water-wave problems involving a freely floating half-immersed cylinder in the presence of a vertical rigid wall. The theory is not able to describe the lowest-frequency resonance, but otherwise yields explicit approximations for the locations of resonances in the complex plane and for their corresponding residues. Two problems are investigated in detail: the time-domain motion following a vertical displacement of the cylinder from equilibrium, and the time-harmonic motion of a cylinder that is excited by an incident plane wave.

JFM classification

Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 581 - 610
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Copyright
© 2016 Cambridge University Press 

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