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Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders

Published online by Cambridge University Press:  20 January 2017

Luke G. Bennetts*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
Malte A. Peter
Affiliation:
Institute of Mathematics, University of Augsburg, 86135 Augsburg, Germany Augsburg Centre for Innovative Technologies, University of Augsburg, 86135 Augsburg, Germany
Fabien Montiel
Affiliation:
Department of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand
*
Email address for correspondence: luke.bennetts@adelaide.edu.au

Abstract

Linear potential-flow theory is used to study loads imposed on finite line arrays of rigid, bottom-mounted, surface-piercing, vertical cylinders by surface water waves. Perturbations in the cylinder locations are shown to damp the resonant loads experienced by the unperturbed array. A relationship is established between the damping and the phenomenon of Anderson localisation. Specifically, the Rayleigh–Bloch waves responsible for the resonant loads are shown to attenuate along the array when perturbations are introduced, resulting in localisation when the attenuation rate is sufficiently large with respect to the array length. Further, an efficient solution method for line arrays is introduced that captures the Rayleigh–Bloch wave modes supported by unperturbed arrays from the scattering characteristics of an individual cylinder.

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Papers
Copyright
© 2017 Cambridge University Press 

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