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

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journal contribution
posted on 26.03.2019, 10:06 by Simone Michele, Emiliano Renzi, Paolo Sammarco
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.

Funding

The work of S. Michele and E. Renzi is supported by a Royal Society - CNR International Fellowship

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fluid Mechanics

Volume

869

Pages

238-263

Citation

MICHELE, S., RENZI, E. and SAMMARCO, P., 2019. Weakly nonlinear theory for a gate-type curved array in waves. Journal of Fluid Mechanics, 869, 25 June 2019 , pp. 238-263.

Publisher

© Cambridge University Press

Version

AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal Journal of Fluid Mechanics and the definitive published version is available at https://doi.org/10.1017/jfm.2019.223

Acceptance date

15/03/2019

Publication date

2019-04-23

Copyright date

2019

ISSN

0022-1120

eISSN

1469-7645

Language

en

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Keywords

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