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Graded resonator arrays for spatial frequency separation and amplification of water waves

Published online by Cambridge University Press:  12 September 2018

Luke G. Bennetts Open the ORCID record for Luke G. Bennetts [Opens in a new window] ,
Malte A. Peter  and
Richard V. Craster
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
Richard V. Craster
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders for wavelengths comparable to the array length and for a range of incident directions. Transfer-matrix analysis is used to attribute the large amplifications to excitation of local Rayleigh–Bloch waves and gradual slowing down of their group velocity along the array.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , R4
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Copyright
© 2018 Cambridge University Press 

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