The interaction of oblique surface gravity waves with multiple bottom-standing flexible porous breakwaters is analyzed based on the linearized theory of water waves. Using the method of eigenfunction expansion and the least square approximation, the wave propagation in the presence of single bottom-standing barriers is analyzed considering the upper edge to be: (i) free and (ii) moored, whereas the lower edge is considered to be clamped at the bottom. The wide-spacing approximation is used to analyze the wave interaction with multiple porous bottom-standing flexible barriers to understand the effect of the submerged flexible barriers as an effective breakwater. A brief comparison of both the upper edge conditions is carried out to analyze the effect of wave dissipation due to the presence of multiple barriers. The numerical results for the reflection and transmission coefficients along with the free surface vertical deflection are obtained for the case of two and three multiple bottom-standing barriers. The attenuation in the wave height due to the presence of porosity, change in barrier depth, and distance between the barriers are analyzed. The present study will be helpful in the analysis of proper functioning of porous bottom-standing barrier as an effective breakwater for the protection of offshore structures.

References

1.
Lee
,
J. F.
, and
Chen
,
C. J.
,
1990
, “
Wave Interaction With Hinged Flexible Breakwater
,”
J. Hydraul. Res.
,
28
, pp.
283
295
.10.1080/00221689009499070
2.
Williams
,
A. N.
,
Geiger
,
P. T.
, and
McDougal
,
W. G.
,
1991
, “
Flexible Floating Breakwater
,”
ASCE J. Waterw., Port, Coastal Ocean Eng.
,
117
, pp.
429
450
.10.1061/(ASCE)0733-950X(1991)117:5(429)
3.
Thompson
,
G. O.
,
Sollitt
,
C. K.
,
McDougal
,
W. G.
, and
Bender
,
W. R.
,
1992
, “
Flexible Membrane Wave Barrier
,”
ASCE Conference Ocean V, College Station
,
TX
, Nov. 2–5, pp.
129
148
.
4.
Isaacson
,
M.
,
1993
, “
Wave Effects on Floating Breakwaters
,”
Proc. Canadian Coastal Conference
, Vancouver, Canada, May 4–8, Vol.
1
, pp.
53
66
.
5.
Abul-Azm
,
A. G.
,
1994
, “
Wave Diffraction by Double Flexible Breakwaters
,”
Appl. Ocean Res.
,
16
, pp.
87
99
.10.1016/0141-1187(94)90005-1
6.
Kim
,
M. H.
, and
Kee
,
S. T.
,
1996
, “
Flexible Membrane Wave Barrier. I: Analytic and Numerical Solutions
,”
ASCE J. Waterw., Port, Coastal Ocean Eng.
,
122
, pp.
46
53
.10.1061/(ASCE)0733-950X(1996)122:1(46)
7.
Kee
,
S. T.
, and
Kim
,
M. H.
,
1997
, “
Flexible Membrane Wave Barrier. II: Floating/Submerged Buoy-membrane System
,”
ASCE J. Waterw., Port, Coastal Ocean Eng.
,
123
, pp.
82
90
.10.1061/(ASCE)0733-950X(1997)123:2(82)
8.
Sahoo
,
T.
,
Lee
,
M. M.
, and
Chwang
,
A. T.
,
2000
, “
Trapping and Generation of Waves by Vertical Porous Structures
,”
J. Eng. Math.
,
126
(
10
), pp.
1074
1082
.10.1061/(ASCE)0733-9399(2000)126:10(1074)
9.
Lee
,
M. M.
, and
Chwang
,
A. T.
,
2000
, “
Scattering and Radiation of Water Waves by Permeable Barriers
,”
Phys. Fluids
,
12
, pp.
54
65
.10.1063/1.870284
10.
Karmakar
,
D.
, and
Sahoo
,
T.
,
2008
, “
Gravity Wave Interaction With Floating Membrane Due to Abrupt Change in Water Depth
,”
Ocean Eng.
,
35
(
7
), pp.
598
615
.10.1016/j.oceaneng.2008.01.009
11.
Karmakar
,
D.
, and
Soares
,
C. G.
,
2012
, “
Oblique Scattering of Gravity Waves by Moored Floating Membrane With Changes in Bottom Topography
,”
Ocean Eng.
,
54
, pp.
87
100
.10.1016/j.oceaneng.2012.07.005
12.
Chwang
,
A. T.
, and
Chan
,
A. T.
,
1998
, “
Interaction Between Porous Media and Wave Motion
,”
Annu. Rev. Fluid Mech.
,
30
, pp.
53
84
.10.1146/annurev.fluid.30.1.53
13.
Molin
,
B.
,
2011
, “
Hydrodynamic Modeling of Perforated Structures
,”
Appl. Ocean Res.
,
33
, pp.
1
11
.10.1016/j.apor.2010.11.003
14.
Wang
,
K. H.
, and
Ren
,
X.
,
1993
, “
Water Waves on Flexible and Porous Breakwaters
,”
ASCE J. Eng. Mech.
,
119
, pp.
1025
1047
.10.1061/(ASCE)0733-9399(1993)119:5(1025)
15.
Yang
,
H. T. Y.
,
Huang
,
L. H.
, and
Hwang
,
W. S.
,
1997
, “
The Interference of a Semi-Submerged Obstacle on the Porous Breakwater
,”
Appl. Ocean Res.
,
19
, pp.
263
273
.10.1016/S0141-1187(97)00035-7
16.
Wu
,
J.
,
Wan
,
Z.
, and
Fang
,
Y.
,
1998
, “
Wave Reflection by a Vertical Wall With a Horizontal Submerged Porous Plate
,”
Ocean Eng.
,
25
, pp.
767
779
.10.1016/S0029-8018(97)00037-1
17.
Liu
,
Y.
, and
Li
,
Y. C.
,
2011
, “
Wave Interaction With a Wave Absorbing Double Curtain-Wall Breakwater
,”
Ocean Eng.
,
38
, pp.
1237
1245
.10.1016/j.oceaneng.2011.05.009
18.
Williams
,
A. N.
,
1996
, “
Floating Membrane Breakwater
,”
ASME J. Offshore Mech. Arct. Eng.
,
118
(
1
), pp.
46
51
.10.1115/1.2828800
19.
Cho
,
I. H.
,
Kee
,
S. T.
, and
Kim
,
M. H.
,
1998
, “
Performance of Dual Flexible Membrane Wave Barriers in Oblique Waves
,”
ASCE J. Waterw., Port, Coastal Ocean Eng.
,
124
, pp.
21
30
.10.1061/(ASCE)0733-950X(1998)124:1(21)
20.
Karmakar
,
D.
,
Bhattacharjee
,
J.
, and
Soares
,
C. G.
,
2013
, “
Scattering of Gravity Waves by Multiple Surface-piercing Floating Membrane
,”
Appl. Ocean Res.
,
39
, pp.
40
52
.10.1016/j.apor.2012.10.001
21.
Lo
,
E. Y. M.
,
1998
, “
Flexible Dual Membrane Wave Barrier
,”
ASCE J. Waterw., Port, Coastal Ocean Eng.
,
124
, pp.
264
271
.10.1061/(ASCE)0733-950X(1998)124:5(264)
22.
Lo
,
E. Y. M.
,
2000
, “
Performance of a Flexible Membrane Wave Barrier of an Infinite Vertical Extent
,”
Coastal Eng.
,
42
, pp.
237
251
.10.1142/S0578563400000110
23.
Lee
,
W. K.
, and
Lo
,
E. Y. M.
,
2002
, “
Surface-penetrating Flexible Membrane Wave Barriers of Finite Draft
,”
Ocean Eng.
,
29
(
14
), pp.
1781
1804
.10.1016/S0029-8018(02)00007-0
24.
Liu
,
Y.
, and
Li
,
Y. C.
,
2011
, “
An Alternative Analytical Solution for Water-Wave Motion Over a Submerged Horizontal Porous Plate
,”
J. Eng. Math.
,
69
, pp.
385
400
.10.1007/s10665-010-9406-8
25.
Evans
,
D. V.
, and
Peter
,
M. A.
,
2011
, “
Asymptotic Reflection of Linear Water Waves by Submerged Horizontal Porous Plates
,”
J. Eng. Math.
,
69
, pp.
135
154
.10.1007/s10665-009-9355-2
26.
Liu
,
Y.
, and
Li
,
H. J.
,
2012
, “
Analysis of Wave Interaction With Submerged Perforated Semi-Circular Breakwaters Through Multipole Method
,”
Appl. Ocean Res.
,
34
, pp.
164
172
.10.1016/j.apor.2011.08.003
27.
Stiassnie
,
M.
,
Naheer
,
E.
, and
Boguslavsky
,
I.
,
1984
, “
Energy Losses Due to Vortex Shedding From the Lower Edge of the Vertical Plate Attacked by Surface Waves
,”
Proc. R. Soc. London, Ser. A
,
396
, pp.
131
142
.10.1098/rspa.1984.0112
28.
Ting
,
F. C. K.
, and
Kim
,
Y. K.
,
1994
, “
Vortex Generation in Water Waves Propagating Over a Submerged Obstacle
,”
Coastal Eng.
,
24
, pp.
23
49
.10.1016/0378-3839(94)90025-6
29.
Yu
,
X.
,
1995
, “
Diffraction of Water Waves by Porous Breakwaters
,”
J. Waterw., Port, Coastal Ocean Eng.
,
121
, pp.
275
282
.10.1061/(ASCE)0733-950X(1995)121:6(275)
30.
Yu
,
X.
, and
Chwang
,
A. T.
,
1994
, “
Wave Motion Through Porous Structures
,”
ASCE J. Eng. Mech.
,
120
(
5
), pp.
989
1008
.10.1061/(ASCE)0733-9399(1994)120:5(989)
You do not currently have access to this content.