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Water-wave trapping by floating circular cylinders

Published online by Cambridge University Press:  25 August 2009

R. PORTER  and
D. V. EVANS
R. PORTER*
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
D. V. EVANS
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
*
†Email address for correspondence: richard.porter@bris.ac.uk
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Abstract

Under the assumptions of the linearized theory of small-amplitude water waves, it is proved that plane waves, normally incident upon a semi-immersed cylinder of uniform circular cross-section floating freely on the surface of a fluid of infinite depth, are capable of being totally reflected. Numerically, this is shown to occur at a single non-dimensional frequency. This remarkable result is used to construct examples of motion-trapped modes, involving pairs of freely floating cylinders moving either in phase or out of phase. The former case is equivalent to having a motion-trapped mode for a single such cylinder next to a rigid vertical wall. In the latter out-of-phase case, the pair of cylinders move as if they form the wetted sections of a single rigidly connected catamaran structure.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 311 - 325
Copyright
Copyright © Cambridge University Press 2009

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References

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