In the field of offshore renewable energy, impermeable plates are used as underwater lenses to amplify the wave amplitude, and perforated plates can harness wave energy as a power takeoff device. Within the framework of the linear potential-flow theory, the water wave scattering by impermeable and perforated horizontal plates is investigated in the present study, and both circular and elliptical plates are considered. The hypersingular integral equation is constructed to model the interaction between water waves and plates of small thickness. For wave scattering by impermeable plates with the focus on wave amplification, wave interference effects due to multiple plates can be utilized to achieve large wave amplification. For perforated plates used for harnessing wave energy, deploying an array of elliptical plates is promising if the deployment line coincides with the major axis and the incident wave propagates along the minor axis. The study gives insight into harnessing energy from water waves by horizontal plates.

1.
Behera
,
H.
, and
Sahoo
,
T.
, “
Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate
,”
J. Fluids Struct.
54
,
643
660
(
2015
).
2.
Bottom
 II,
R. G.
,
Borazjani
,
I.
,
Blevins
,
E. L.
, and
Lauder
,
G. V.
, “
Hydrodynamics of swimming in stingrays: Numerical simulations and the role of the leading-edge vortex
,”
J. Fluid Mech.
788
,
407
443
(
2016
).
3.
Chen
,
X. B.
, “
Evaluation de la fonction de green du probleme de diffraction/radiation en profondeur d'eau finie-Une nouvelle méthode rapide et précise
,” in
Actes Des 4e Journées de L'Hydrodynamique, Nantes, France
(
1993
), pp.
371
384
.
4.
Chwang
,
A. T.
, “
A porous-wavemaker theory
,”
J. Fluid Mech.
132
,
395
406
(
1983
).
5.
Chwang
,
A. T.
, and
Chan
,
A. T.
, “
Interaction between porous media and wave motion
,”
Annu. Rev. Fluid Mech.
30
,
53
84
(
1998
).
6.
Faltinsen
,
O. M.
,
Sea Loads on Ships and Offshore Structures
(
Cambridge University Press
,
1993
).
7.
Hariri Nokob
,
M.
, and
Yeung
,
R. W.
, “
Diffraction and radiation loads on open cylinders of thin and arbitrary shapes
,”
J. Fluid Mech.
772
,
649
677
(
2015
).
8.
Huang
,
Z.
,
Li
,
Y.
, and
Liu
,
Y.
, “
Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review
,”
Ocean Eng.
38
,
1031
1053
(
2011
).
9.
Li
,
Z. F.
,
Wu
,
G. X.
, and
Ji
,
C. Y.
, “
Interaction of wave with a body submerged below an ice sheet with multiple arbitrarily spaced cracks
,”
Phys. Fluids
30
,
057107
(
2018a
).
10.
Li
,
Z. F.
,
Wu
,
G. X.
, and
Shi
,
Y. Y.
, “
Wave diffraction by a circular crack in an ice sheet floating on water of finite depth
,”
Phys. Fluids
30
,
117103
(
2018b
).
11.
Liang
,
H.
,
Ouled Housseine
,
C.
,
Chen
,
X. B.
, and
Shao
,
Y.
, “
Efficient methods free of irregular frequencies in wave and solid/porous structure interactions
,”
J. Fluids Struct.
98
,
103130
(
2020
).
12.
Liang
,
H.
,
Shao
,
Y.
, and
Chen
,
J.
, “
Higher-order derivatives of the Green function in hyper-singular integral equations
,”
Eur. J. Mech.-B/Fluids
86
,
223
230
(
2021
).
13.
Liu
,
Y.
,
Cong
,
P.
,
Gou
,
Y.
,
Yoshida
,
S.
, and
Kashiwagi
,
M.
, “
Enhanced Endo's approach for evaluating free-surface Green's function with application to wave-structure interactions
,”
Ocean Eng.
207
,
107377
(
2020
).
14.
Mackay
,
E. B. L.
, “
Consistent expressions for the free-surface Green function in finite water depth
,”
Appl. Ocean Res.
93
,
101965
(
2019
).
15.
Mackay
,
E. B. L.
,
Liang
,
H.
, and
Johanning
,
L.
, “
A BEM model for wave forces on structures with thin porous elements
,”
J. Fluids Struct.
102
,
103246
(
2021
).
16.
Martin
,
P. A.
, and
Farina
,
L.
, “
Radiation of water waves by a heaving submerged horizontal disc
,”
J. Fluid Mech.
337
,
365
379
(
1997
).
17.
Mei
,
C. C.
,
Stiassnie
,
M.
, and
Yue
,
D. K. P.
,
Theory and Applications of Ocean Surface Waves
, 3rd ed. (
World Scientific
,
2017
).
18.
Meylan
,
M. H.
,
Bennetts
,
L. G.
,
Cavaliere
,
C.
,
Alberello
,
A.
, and
Toffoli
,
A.
, “
Experimental and theoretical models of wave-induced flexure of a sea ice floe
,”
Phys. Fluids
27
,
041704
(
2015
).
19.
Meylan
,
M. H.
,
Bennetts
,
L. G.
, and
Peter
,
M. A.
, “
Water-wave scattering and energy dissipation by a floating porous elastic plate in three dimensions
,”
Wave Motion
70
,
240
250
(
2017
).
20.
Molin
,
B.
,
Hydrodynamique Des Structures Offshore
(
Editions Technip
,
2002
).
21.
Molin
,
B.
, “
Hydrodynamic modeling of perforated structures
,”
Appl. Ocean Res.
33
,
1
11
(
2011
).
22.
Newman
,
J. N.
,
Marine Hydrodynamics
(
Massachusetts Institute of Technology Press
,
1977
).
23.
Newman
,
J. N.
, “
Algorithms for the free-surface Green function
,”
J. Eng. Math.
19
,
57
67
(
1985
).
24.
Newman
,
J. N.
, “
Amplification of waves by submerged plates
,” in
Proceedings of the 30th International Workshop on Water Waves and Floating Bodies, Bristol, UK
, edited by
R.
Porter
and
J.
Zang
(
2015
), pp.
153
156
.
25.
Parsons
,
N. F.
, and
Martin
,
P. A.
, “
Scattering of water waves by submerged plates using hypersingular integral equations
,”
Appl. Ocean Res.
14
,
313
321
(
1992
).
26.
Porter
,
R.
, “
Linearised water wave problems involving submerged horizontal plates
,”
Appl. Ocean Res.
50
,
91
109
(
2015
).
27.
Renzi
,
E.
, “
Hydroelectromechanical modelling of a piezoelectric wave energy converter
,”
Proc. R. Soc. A
472
,
20160715
(
2016
).
28.
Renzi
,
E.
, and
Dias
,
F.
, “
Resonant behaviour of an oscillating wave energy converter in a channel
,”
J. Fluid Mech.
701
,
482
510
(
2012
).
29.
Sarkar
,
D.
,
Renzi
,
E.
, and
Dias
,
F.
, “
Wave farm modelling of oscillating wave surge converters
,”
Proc. R. Soc. A
470
,
20140118
(
2014
).
30.
Selvan
,
S. A.
,
Gayathri
,
R.
,
Behera
,
H.
, and
Meylan
,
M. H.
, “
Surface wave scattering by multiple flexible fishing cage system
,”
Phys. Fluids
33
,
037119
(
2021
).
31.
Stamnes
,
J. J.
,
Løvhaugen
,
O.
,
Spjelkavik
,
B.
,
Mei
,
C. C.
,
Lo
,
E.
, and
Yue
,
D. K. P.
, “
Nonlinear focusing of surface waves by a lens–theory and experiment
,”
J. Fluid Mech.
135
,
71
94
(
1983
).
32.
Wang
,
C.
, and
Zhang
,
Y.
, “
Hydrodynamic performance of an offshore oscillating water column device mounted over an immersed horizontal plate: A numerical study
,”
Energy
222
,
119964
(
2021
).
33.
Wehausen
,
J. V.
, and
Laitone
,
E. V.
, “
Surface waves
,”
Hanbuch Phys.
9
,
446
778
(
1960
).
34.
Zheng
,
S.
,
Meylan
,
M. H.
,
Greaves
,
D.
, and
Iglesias
,
G.
, “
Water-wave interaction with submerged porous elastic disks
,”
Phys. Fluids
32
,
047106
(
2020a
).
35.
Zheng
,
S.
,
Meylan
,
M. H.
,
Zhu
,
G.
,
Greaves
,
D.
, and
Iglesias
,
G.
, “
Hydroelastic interaction between water waves and an array of circular floating porous elastic plates
,”
J. Fluid Mech.
900
,
A20
(
2020b
).
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