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Weakly nonlinear theory for a gate-type curved array in waves

Published online by Cambridge University Press:  23 April 2019

S. Michele Open the ORCID record for S. Michele [Opens in a new window] ,
E. Renzi  and
P. Sammarco
S. Michele*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
E. Renzi
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
P. Sammarco
Affiliation:
Department of Civil Engineering and Computer Science, Università degli Studi di Roma ‘Tor Vergata’, Via del Politecnico 1, 00133 Roma, Italy
*
†Email address for correspondence: s.michele@lboro.ac.uk
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Abstract

We analyse the effect of gate surface curvature on the nonlinear behaviour of an array of gates in a semi-infinite channel. Using a perturbation-harmonic expansion, we show the occurrence of new detuning and damping terms in the Ginzburg–Landau evolution equation, which are not present in the case of flat gates. Unlike the case of linearised theories, synchronous excitation of trapped modes is now possible because of interactions between the wave field and the curved boundaries at higher orders. Finally, we apply the theory to the case of surging wave energy converters (WECs) with curved geometry and show that the effects of nonlinear synchronous resonance are substantial for design purposes. Conversely, in the case of subharmonic resonance we show that the effects of surface curvature are not always beneficial as previously thought.

JFM classification

Geophysical and Geological Flows: Coastal engineering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , pp. 238 - 263
Copyright
© 2019 Cambridge University Press 

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