Abstract

The study evaluates the hydrodynamic performance of quarter-circular breakwater (QCB) with various types of porous shields (say retrofits) under incident waves. The QCB with (i) vertical shield, (ii) seaside quarter-circular retrofit (QCR), (iii) shoreside QCR, and (iv) partial rectangular retrofit (PRR) are proposed to enhance the performance of QCB. The effect of porous shields is analyzed using the quadratic pressure drop condition and dual boundary element method (DBEM) under the framework of linearized potential flow theory. Study results are validated with the available results reported by the authors after some numerical modifications. The effect of shield porosity, and wave height on the reflection, transmission, energy loss, and vertical and horizontal forces on QCB and shield are reported as a function of relative water depth. A comparative study is performed among all the proposed breakwaters to identify an effective configuration against the incident waves. Around 39%, 30%, 31%, and 56% reduction of wave transmission is obtained for QCB with vertical shield, seaside, shoreside QCR, and PRR, respectively, when compared with QCB alone for kh=1. The wave transmission KT=0.16 and energy loss KL=0.95 are obtained when kh=2 with the addition of the PRR for a QCB, which is observed as an effective porous shield against the incident waves when compared with the other types of shields. The 10–20% retrofit porosity is recommended with clear spacing b/h=0.9 and the QCB radius of R2/h=0.7 for the effective distribution of the scattering coefficients against the incident waves.

References

1.
Panduranga
,
K.
,
Koley
,
S.
, and
Sahoo
,
T.
,
2021
, “
Surface Gravity Wave Scattering by Multiple Slatted Screens Placed Near a Caisson Porous Breakwater in the Presence of Seabed Undulations
,”
Appl. Ocean Res.
,
111
, p.
102675
.
2.
Dhanunjaya
,
E.
,
Sanjeeva Rayudu
,
E.
, and
Venkateswarlu
,
V.
,
2024
, “
Hydrodynamic Performance of an Array of Stratified Pile Rock Breakwaters Placed on Elevated Seabed
,”
ASME J. Offshore Mech. Arct. Eng.
,
146
(
4
), p.
042101
.
3.
Yueh
,
C. Y.
, and
Chuang
,
S. H.
,
2012
, “
A Boundary Element Model for a Partially Piston-Type Porous Wave Energy Converter in Gravity Waves
,”
Eng. Anal. Boundary Elem.
,
36
(
5
), pp.
658
664
.
4.
Sankarbabu
,
K.
,
Sannasiraj
,
S. A.
, and
Sundar
,
V.
,
2007
, “
Interaction of Regular Waves With a Group of Dual Porous Circular Cylinders
,”
Appl. Ocean Res.
,
29
(
4
), pp.
180
190
.
5.
Dhinakaran
,
G.
,
Sundar
,
V.
, and
Sundaravadivelu
,
R.
,
2012
, “
Review of the Research on Emerged and Submerged Semicircular Breakwaters
,”
Proc. Inst. Mech. Eng., Part M: J. Eng. Marit. Environ.
,
226
(
4
), pp.
397
409
.
6.
Tsai
,
C. C.
,
Behera
,
H.
, and
Hsu
,
T. W.
,
2023
, “
Analysis of Water Wave Interaction With Multiple Submerged Semi-Circular Porous Structures
,”
Arch. Appl. Mech.
,
93
(
7
), pp.
2693
2709
.
7.
Xie
,
S. L.
,
Li
,
Y. B.
,
Wu
,
Y. Q.
, and
Gu
,
B. B.
,
2006
, “
Preliminary Research on Wave Forces on Quarter Circular Breakwater
,”
Ocean Eng.
,
24
(
1
), pp.
14
18
.
8.
Lyu
,
Z.
,
Liu
,
Y.
,
Li
,
H.
, and
Mori
,
N.
,
2020
, “
Iterative Multipole Solution for Wave Interaction With Submerged Partially Perforated Semi-Circular Breakwater
,”
Appl. Ocean Res.
,
97
, p.
102103
.
9.
Forbes
,
L. K.
, and
Schwartz
,
L. W.
,
1982
, “
Free-Surface Flow Over a Semicircular Obstruction
,”
J. Fluid Mech.
,
114
(
1
), pp.
299
314
.
10.
Zhang
,
N. C.
,
Wang
,
L. Q.
, and
Yu
,
Y. X.
,
2005
, “
Oblique Irregular Waves Load on Semicircular Breakwater
,”
Coastal Eng. J.
,
47
(
4
), pp.
183
204
.
11.
Aburatani
,
S.
,
Koizuka
,
T.
,
Sasayama
,
H.
,
Tanimoto
,
K.
, and
Namerikawa
,
N.
,
1996
, “
Field Test on a Semi-Circular Caisson Breakwater
,”
Coastal Eng. Japan
,
39
(
1
), pp.
59
78
.
12.
Sasmal
,
A.
, and
De
,
S.
,
2024
, “
Mitigation of Wave Force and Dissipation of Energy by Multiple Arbitrary Porous Barriers
,”
Waves Random Complex Media
,
34
(
2
), pp.
523
546
.
13.
Praveen
,
K. M.
,
Venkateswarlu
,
V.
, and
Karmakar
,
D.
,
2022
, “
Hydroelastic Response of Floating Elastic Plate in the Presence of Vertical Porous Barriers
,”
Ships Offshore Struct.
,
17
(
2
), pp.
457
471
.
14.
Singh
,
M.
, and
Gayen
,
R.
,
2022
, “
Scattering of Linear Gravity-Capillary Waves by a Completely Submerged Vertical Porous Elastic Plate
,”
Waves Random Complex Media
, pp.
1
21
.
15.
Vijay
,
K. G.
,
Venkateswarlu
,
V.
, and
Sahoo
,
T.
,
2021
, “
Bragg Scattering of Surface Gravity Waves by an Array of Submerged Breakwaters and a Floating Dock
,”
Wave Motion
,
106
, p.
102807
.
16.
Sahoo
,
G.
,
Singla
,
S.
, and
Martha
,
S. C.
,
2023
, “
Mitigation of Wave Impact on Sea Wall by a Floating Elastic Plate and a Porous Structure
,”
ASME J. Offshore Mech. Arct. Eng.
,
145
(
5
), p.
051202
.
17.
Venkateswarlu
,
V.
,
Sanjeeva Rayudu
,
E.
,
Dhanunjaya
,
E.
, and
Vijay
,
K. G.
,
2023
, “
Wave Action Analysis of Multiple Bottom Fixed Semi-Circular Breakwaters in the Presence of a Floating Dock
,”
ASME J. Offshore Mech. Arct. Eng.
,
145
(
6
), p.
061201
.
18.
Li
,
X.
,
Wang
,
L.
,
Wang
,
Q.
,
Xie
,
T.
,
You
,
Z.
,
Song
,
K.
, and
Wang
,
Y.
,
2021
, “
A Comparative Study of the Hydrodynamic Characteristics of Permeable Twin-Flat-Plate and Twin-Arc-Plate Breakwaters Based on Physical Modeling
,”
Ocean Eng.
,
219
, p.
108270
.
19.
Neelamani
,
S.
, and
Al-Anjari
,
N.
,
2021
, “
Experimental Investigations on Wave-Induced Dynamic Pressures Over Slotted Vertical Barriers in Random Wave Fields
,”
Ocean Eng.
,
220
, p.
108482
.
20.
Nicholson
,
J.
,
Broker
,
I.
,
Roelvink
,
J. A.
,
Price
,
D.
,
Tanguy
,
J. M.
, and
Moreno
,
L.
,
1997
, “
Inter Comparison of Coastal Area Morphodynamic Models
,”
Coastal Eng.
,
31
(
1–4
), pp.
97
123
.
21.
Sharma
,
P.
,
Sarkar
,
B.
, and
De
,
S.
,
2024
, “
Oblique Wave Scattering by Single and Double Inverse T-Type Breakwaters
,”
Ocean Eng.
,
303
, p.
117804
.
22.
Sharma
,
P.
,
Sarkar
,
B.
, and
De
,
S.
,
2025
, “
Oblique Wave Scattering by a Pair of Asymmetric Inverse Π-Shaped Breakwater
,”
ASME J. Offshore Mech. Arct. Eng.
,
147
(
4
), p.
041201
.
23.
Jarlan
,
G. E.
,
1961
, “
A Perforated Wall Breakwater
,”
Dock. Harbour Auth.
,
41
(
486
), pp.
394
398
.
24.
Molin
,
B.
, and
Remy
,
F.
,
2015
, “
Inertia Effects in TLD Sloshing With Perforated Screens
,”
J. Fluids Struct.
,
59
, pp.
165
177
.
25.
Li
,
A. J.
,
Liu
,
Y.
, and
Lyu
,
Z. R.
,
2020
, “
Analysis of Water Wave Interaction With a Submerged Quarter-Circular Breakwater Using Multipole Method
,”
Proc. Inst. Mech. Eng., Part M: J. Eng. Marit. Environ.
,
234
(
4
), pp.
846
860
.
26.
Venkateswaralu
,
V.
,
Vijay
,
K. G.
,
Nishad
,
C. S.
, and
Sahoo
,
T.
,
2022
, “
Gravity Wave Scattering by Retrofitted Circular Breakwaters Using Dual Boundary Integral Formulation
,”
Ocean Eng.
,
265
, p.
112259
.
27.
Lyu
,
Z.
,
Liu
,
Y.
,
Li
,
H.
, and
Mori
,
N.
,
2024
, “
Multipole Solution With Nonlinear Pressure Loss for Oblique Waves Action on a Submerged Partially Perforated Semi-Circular Breakwater
,”
Ocean Eng.
,
291
, p.
116487
.
28.
Liu
,
Y.
, and
Li
,
H. J.
,
2017
, “
Iterative Multi-Domain BEM Solution for Water Wave Reflection by Perforated Caisson Breakwaters
,”
Eng. Anal. Boundary Elem.
,
77
, pp.
70
80
.
29.
Hong
,
H. K.
, and
Chen
,
J. T.
,
1988
, “
Derivations of Integral Equations of Elasticity
,”
J. Eng. Mech.
,
114
(
6
), pp.
1028
1044
.
30.
Chen
,
J. T.
,
Hong
,
H. K.
, and
Chyuan
,
S. W.
,
1994
, “
Boundary Element Analysis and Design in Seepage Problems Using Dual Integral Formulation
,”
Finite Elem. Anal. Des.
,
17
(
1
), pp.
1
20
.
31.
Chen
,
K. H.
,
Chen
,
J. T.
,
Lin
,
S. Y.
, and
Lee
,
Y. T.
,
2004
, “
Dual Boundary Element Analysis of Normal Incident Wave Passing a Thin Submerged Breakwater With Rigid, Absorbing, and Permeable Boundaries
,”
J. Waterw. Port Coastal Ocean Eng.
,
130
(
4
), pp.
179
190
.
32.
Chen
,
J. T.
,
Yueh
,
C. Y.
,
Chang
,
Y. L.
, and
Wen
,
C. C.
,
2017
, “
Why Dual Boundary Element Method Is Necessary?
,”
Eng. Anal. Boundary Elem.
,
76
, pp.
59
68
.
33.
Zhao
,
Y.
,
Liu
,
Y.
,
Li
,
H. J.
, and
Chang
,
A. T.
,
2020
, “
Iterative Dual BEM Solution for Water Wave Scattering by Breakwaters Having Perforated Thin Plates
,”
Eng. Anal. Boundary Elem.
,
120
, pp.
95
106
.
34.
Vijay
,
K. G.
,
Venkateswarlu
,
V.
, and
Nishad
,
C. S.
,
2021
, “
Wave Scattering by Inverted Trapezoidal Porous Boxes Using Dual Boundary Element Method
,”
Ocean Eng.
,
219
, p.
108149
.
35.
Mackay
,
E.
, and
Johanning
,
L.
,
2020
, “
Comparison of Analytical and Numerical Solutions for Wave Interaction With a Vertical Porous Barrier
,”
Ocean Eng.
,
199
, p.
107032
.
36.
Suh
,
K. D.
,
Ji
,
C. H.
, and
Kim
,
B. H.
,
2011
, “
Closed-Form Solutions for Wave Reflection and Transmission by Vertical Slotted Barrier
,”
Coastal Eng.
,
58
(
12
), pp.
1089
1096
.
37.
Huang
,
Z.
,
Li
,
Y.
, and
Liu
,
Y.
,
2011
, “
Hydraulic Performance and Wave Loadings of Perforated/Slotted Coastal Structures: A Review
,”
Ocean Eng.
,
38
(
10
), pp.
1031
1053
.
38.
Liu
,
Y.
,
Li
,
H. J.
, and
Zhu
,
L.
,
2016
, “
Bragg Reflection of Water Waves by Multiple Submerged Semi-Circular Breakwaters
,”
Appl. Ocean Res.
,
56
, pp.
67
78
.
39.
Swaminathan
,
K. R.
,
Sundar
,
V.
, and
Sannasiraj
,
S. A.
,
2022
, “
Hydrodynamic Characteristics of Concave Front Pile-Supported Breakwaters With a Tubular Wave Screen
,”
J. Waterw. Port Coastal Ocean Eng.
,
148
(
1
), p.
04021041
.
40.
AlYousif
,
A.
,
Neelamani
,
S.
, and
Valle-Levinson
,
A.
,
2021
, “
Hydrodynamic Performance of Tire-Based Floating Breakwater
,”
Marine Georesour. Geotechnol.
,
39
(
9
), pp.
1025
1043
.
41.
Lokesha
,
S. V.
, and
Annamalaisamy
,
S. S.
,
2020
, “
Transmission and Reflection Characteristics of Perforated Submerged Single and Multiple Artificial Reef Units
,”
ASME J. Offshore Mech. Arct. Eng.
,
142
(
5
), p.
051301
.
You do not currently have access to this content.