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Water waves over arrays of horizontal cylinders: band gaps and Bragg resonance

Published online by Cambridge University Press:  25 January 2011

C. M. LINTON
C. M. LINTON*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
*
†Email address for correspondence: c.m.linton@lboro.ac.uk
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Abstract

The existence of a band-gap structure associated with water waves propagating over infinite periodic arrays of submerged horizontal circular cylinders in deep water is established. Waves propagating at right angles to the cylinder axes and at an oblique angle are both considered. In each case an exact linear analysis is presented with numerical results obtained by solving truncated systems of equations. Calculations for large finite arrays are also presented, which show the effect of an incident wave having a frequency within a band gap – with the amount of energy transmitted across the array tending to zero as the size of the array is increased. The location of the band gaps is not as predicted by Bragg's law, but we show that an approximate determination of their position can be made very simply if the phase of the transmission coefficient for a single cylinder is known.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 504 - 526
Copyright
Copyright © Cambridge University Press 2011

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