The near trapping phenomena are associated with the wave trapping in arrays of large number of solid bodies, which experience increased amplitudes of free-surface elevation between adjacent bodies, and corresponding large wave loads on each array element. In relevant situations of infinite arrays, the wave energy is trapped within the array allowing only a small amount of energy to radiate to the far field, forming the so-called trapped mode phenomenon. The question which this paper tries to answer is whether trapped waves are simulated by arrays of porous vertical cylinders. To tackle this task, a solution method that solves the corresponding diffraction problem by the application of the multiple scattering approach, for the simulation of the hydrodynamic interactions between the waves and the elements of the array, is proposed. Numerical results for several geometrical configurations are presented and discussed, highlighting the effect of porous cylinders on the exerted hydrodynamic loads on the array.
REFERENCES
1.
F.
Ursell
, “
Trapping modes in the theory of surface waves
,” Math. Proc. Camb. Phil. Soc.
47
(2
), 347
–358
(1951
).2.
D. V.
Evans
and
C. M.
Linton
, “
Trapped modes in open channels
,” J. Fluid Mech.
225
, 153
–175
(1991
).3.
M.
Callan
,
C. M.
Linton
, and
D. V.
Evans
, “
Trapped modes in two-dimensional waveguides
,” J. Fluid Mech.
229
, 51
–64
(1991
).4.
D. V.
Evans
,
M.
Levitin
, and
D.
Vassiliev
, “
Existence theorems for trapped modes
,” J. Fluid Mech.
261
, 21
–31
(1994
).5.
H. D.
Maniar
and
J. N.
Newman
, “
Wave diffraction by a long array of cylinders
,” J. Fluid Mech.
339
, 309
–330
(1997
).6.
D. V.
Evans
and
R.
Porter
, “
Near-trapping of waves by circular arrays of vertical cylinders
,” Appl. Ocean Res.
19
, 83
–99
(1997
).7.
S.
Malenica
,
R.
Eatock Taylor
, and
J. B.
Huang
, “
Second-order water wave diffraction by an array of vertical cylinders
,” J. Fluid Mech.
390
, 349
–373
(1999
).8.
D. V.
Evans
and
R.
Porter
, “
Trapping and near-trapping by arrays of cylinders in waves
,” J. Eng. Math.
35
, 149
–179
(1999
).9.
P.
McIver
, “
Water-wave propagation through an infinite array of cylindrical structures
,” J. Fluid Mech.
424
, 101
–125
(2000
).10.
D. A. G.
Walker
and
R.
Eatock Taylor
, “
Wave diffraction from linear arrays of cylinders
,” Ocean Eng.
32
(17–18
), 2053
–2078
(2005
).11.
D. A. G.
Walker
,
R.
Eatock Taylor
,
P. H.
Taylor
, and
J.
Zang
, “
Wave diffraction and near-trapping by a multi-column gravity-based structure
,” Ocean Eng.
35
(2
), 201
–229
(2008
).12.
J. R.
Grice
,
P. H.
Taylor
, and
R.
Eatock Taylor
, “
Near-trapping effects for multi-column structures in deterministic and random waves
,” Ocean Eng.
58
, 60
–77
(2013
).13.
Z.
Wang
,
G.
He
,
Z.
Zhang
, and
Y.
Meng
, “
Viscous-flow-based analysis of wave near-trapped in a four-cylinder structure
,” J. Mar. Sci. Appl.
17
, 371
–379
(2018
).14.
M. H.
Meylan
and
R.
Eatock Taylor
, “
Time-dependent water-wave scattering by arrays of cylinders and the approximation of near trapping
,” J. Fluid Mech.
631
, 103
–125
(2009
).15.
W.
Bai
,
X.
Feng
,
R.
Eatock Taylor
, and
K. K.
Ang
, “
Fully nonlinear analysis of near-trapping phenomenon around an array of cylinders
,” Appl. Ocean Res.
44
, 71
–81
(2014
).16.
I. K.
Chatjigeorgiou
and
V.
Katsardi
, “
Hydrodynamics and near trapping effects in arrays of multiple elliptical cylinders in waves
,” Ocean Eng.
157
, 121
–139
(2018
).17.
I.
Chatjigeorgiou
,
K.
Chatziioannou
, and
T.
Mazarakos
, “
Near trapped modes in long array of truncated circular cylinders
,” J. Waterway, Port, Coastal, Ocean Eng.
145
(1
), 04018035
(2019
).18.
D.
Ning
,
J.
Xu
,
L.
Chen
,
P.
Cong
,
M.
Zhao
, and
C.
Jiang
, “
Boussinesq modelling of near-trapping in a four-cylinder array
,” Ocean Eng.
248
, 110767
(2022
).19.
I. K.
Chatjigeorgiou
, “
Semi-analytical solution for the water diffraction by arrays of truncated circular cylinders in front of a vertical wall
,” Appl. Ocean Res.
88
, 147
–159
(2019
).20.
D. N.
Konispoliatis
,
I. K.
Chatjigeorgiou
, and
S. A.
Mavrakos
, “
Near trapped wave phenomena in an array of truncated cylinder in a perpendicular arrangement in front of a vertical breakwater
,” Appl. Math. Modell.
83
, 497
–525
(2020
).21.
Y. F.
Yang
and
C. Z.
Wang
, “
Finite element analysis of second order wave resonance by multiple cylinders in a uniform current
,” Appl. Ocean Res.
100
, 102132
(2020
).22.
C. O. G.
Ohl
,
R.
Eatock Taylor
,
P. H.
Taylor
, and
A. G. L.
Borthwick
, “
Water wave diffraction by a cylinder array. Part 1. Regular waves
,” J. Fluid Mech.
442
, 1
–32
(2001
).23.
C. O. G.
Ohl
,
P. H.
Taylor
,
R.
Eatock Taylor
, and
A. G. L.
Borthwick
, “
Water wave diffraction by a cylinder array. Part 2. Irregular waves
,” J. Fluid Mech.
442
, 33
–66
(2001
).24.
P.
Cong
,
Y.
Gou
,
B.
Teng
,
K.
Zhang
, and
Y.
Huang
, “
Model experiments on wave elevation around a four-cylinder structure
,” Ocean Eng.
96
, 40
–55
(2015
).25.
R.
Porter
and
D. V.
Evans
, “
Water-wave trapping by floating circular cylinders
,” J. Fluid Mech.
633
, 311
–325
(2009
).26.
H. A.
Wolgamot
,
R.
Eatock Taylor
, and
P. H.
Taylor
, “
Radiation, trapping and near-trapping in arrays of floating truncated cylinders
,” J. Eng. Math.
91
, 17
–35
(2015
).27.
F.
Fabregas Flavia
,
C.
McNatt
,
F.
Rongere
,
A.
Babarit
, and
A. H.
Clement
, “
A numerical tool for the frequency domain simulation of large arrays of identical floating bodies in waves
,” Ocean Eng.
148
, 299
–311
(2018
).28.
C.
Sollitt
and
R.
Cross
, “
Wave reflection and transmission at permeable breakwaters
,” Technical Paper 76-8
(
US Army Corps of Engineers, Coastal Engineering Research Centre
, 1976
).29.
O.
Madsen
, “
Wave transmission through porous structures
,” J. Waterw. Ports Coastal Eng. Div.
100
, 169
–188
(1974
).30.
W.
Sulisz
, “
Wave reflection and transmission at permeable breakwaters of arbitrary cross section
,” Coastal Eng.
9
, 371
–386
(1985
).31.
A. N.
Williams
and
W.
Li
, “
Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders
,” Ocean Eng.
27
, 841
–866
(2000
).32.
M. S.
Park
,
W.
Koo
, and
Y.
Choi
, “
Hydrodynamic interaction with an array of porous circular cylinders
,” Int. J. Nav. Archit. Ocean Eng.
2
, 146
–154
(2010
).33.
F. F.
Zhao
,
T.
Kinoshita
,
W. G.
Bao
,
L. Y.
Huang
,
Z. L.
Liang
, and
R.
Wan
, “
Interaction between waves and an array of floating porous circular cylinders
,” China Ocean Eng.
26
, 397
–412
(2012
).34.
M. S.
Park
and
W.
Koo
, “
Mathematical modeling of partial-porous circular cylinders with water waves
,” Math. Problems Eng.
2015
, 903748
.35.
G. Y.
Wang
,
M. H.
Zhang
,
H. Q.
Zhang
, and
F. J.
Yu
, “
Wave diffraction from an array of porous cylinders with porous plates fixed inside
,” Ocean Eng.
245
, 110327
(2022
).36.
D.
Konispoliatis
and
S.
Mavrakos
, “
Mean drift wave forces on arrays of bodies surrounded by thin porous surfaces
,” J. Mar. Sci. Eng.
11
, 1269
(2023
).37.
K.
Kokkinowrachos
,
S.
Mavrakos
, and
S.
Asorakos
, “
Behavior of vertical bodies of revolution in waves
,” Ocean Eng.
13
(6
), 505
–538
(1986
).38.
S. A.
Mavrakos
and
P.
Koumoutsakos
, “
Hydrodynamic interaction among vertical axisymmetric bodies restrained in waves
,” Appl. Ocean Res.
9
(3
), 128
–140
(1987
).39.
S. A.
Mavrakos
and
P.
McIver
, “
Comparison of methods for computing hydrodynamic characteristics of arrays of wave power devices
,” Appl. Ocean Res.
19
, 283
–291
(1997
).40.
A.
Mavrakos
,
D.
Konispoliatis
,
D.
Ntouras
,
G.
Papadakis
, and
S.
Mavrakos
, “
Hydrodynamic coefficients in heave of a moonpool type floater using theoretical, numerical and CFD methodologies
,” Ocean Eng.
279
, 114519
(2023
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.