Abstract

The purpose of the present study is to reduce the high wave load on a sea wall by utilizing an elastic plate (EP) kept at fixed distance from a porous structure (PS). Thin plate theory is used to model the flow past EP, while Sollit and Cross theory is used to model the flow past PS. A linear potential theory-based analytical solution to the current problem is developed using the eigenfunction expansion technique. To understand the effect of PS and EP in creating tranquility zone and minimum wave loads on the rigid wall, horizontal wave force on the wall, reflection coefficient, dissipation coefficient, and free surface elevation are computed and analyzed for different values of width and friction factor of PS, flexural rigidity and length of EP, angle of incidence, and distance between PS and EP, and the distance between EP and rigid wall. The study demonstrates that both structures considerably reduce the stress on the rigid wall and the wave reflection. It is found that the force on the wall shifted to the left as the width and frictional factor of PS increased. Furthermore, it is observed that PS effectively minimizes the free surface elevation in the region between EP and the wall. It is also found that an effective tranquility zone may be produced, which will put less wave force on the rigid wall, with sufficient spacing between PS and EP, and EP and the wall. The given model is expected to assist in preserving various coastal assets significantly.

References

1.
Lu
,
L.
,
Teng
,
B.
,
Sun
,
L.
, and
Chen
,
B.
,
2011
, “
Modelling of Multi-Bodies in Close Proximity Under Water Waves–Fluid Forces on Floating Bodies
,”
Ocean. Eng.
,
38
(
13
), pp.
1403
1416
.
2.
Zhu
,
D. T.
,
Wang
,
X. G.
, and
Liu
,
Q. J.
,
2017
, “
Conditions and Phase Shift of Fluid Resonance in Narrow Gaps of Bottom Mounted Caissons
,”
China Ocean Eng.
,
31
(
6
), pp.
724
735
.
3.
Gayathri
,
R.
,
Khan
,
M. B. M.
, and
Behera
,
H.
,
2022
, “
Attenuation of Wave Force on a Floating Dock by Multiple Porous Breakwaters
,”
Eng. Anal. Boundary Elements
,
143
, pp.
170
189
.
4.
Chwang
,
A. T.
, and
Chan
,
A. T.
,
1998
, “
Interaction Between Porous Media and Wave Motion
,”
Annu. Rev. Fluid. Mech.
,
30
(
1
), pp.
53
84
.
5.
Karmakar
,
D.
, and
Soares
,
C. G.
,
2014
, “
Wave Transformation Due to Multiple Bottom-Standing Porous Barriers
,”
Ocean. Eng.
,
80
, pp.
50
63
.
6.
Koley
,
S.
,
Mondal
,
R.
, and
Sahoo
,
T.
,
2018
, “
Fredholm Integral Equation Technique for Hydroelastic Analysis of a Floating Flexible Porous Plate
,”
Eur. J.f Mech.-B/Fluids
,
67
, pp.
291
305
.
7.
Singla
,
S.
,
Sahoo
,
T.
,
Martha
,
S. C.
, and
Behera
,
H.
,
2019
, “
Effect of a Floating Permeable Plate on the Hydroelastic Response of a Very Large Floating Structure
,”
J. Eng. Math.
,
116
(
1
), pp.
49
72
.
8.
Mondal
,
D.
, and
Banerjea
,
S.
,
2016
, “
Scattering of Water Waves by an Inclined Porous Plate Submerged in Ocean With Ice Cover
,”
Quart. J. Mech. Appl. Math.
,
69
(
2
), pp.
195
213
.
9.
Yip
,
T. L.
, and
Chwang
,
A. T.
,
1998
, “
Water Wave Control by Submerged Pitching Porous Plate
,”
J. Eng. Mech.
,
124
(
4
), pp.
428
434
.
10.
Evans
,
D. V.
, and
Peter
,
M. A.
,
2011
, “
Asymptotic Reflection of Linear Water Waves by Submerged Horizontal Porous Plates
,”
J. Eng. Math.
,
69
(
2
), pp.
135
154
.
11.
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
(
4
), pp.
385
400
.
12.
Gayen
,
R.
, and
Mondal
,
A.
,
2014
, “
A Hypersingular Integral Equation Approach to the Porous Plate Problem
,”
Appl. Ocean. Res.
,
46
, pp.
70
78
.
13.
Renzi
,
E.
,
2016
, “
Hydroelectromechanical Modelling of a Piezoelectric Wave Energy Converter
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
472
(
2195
), p.
20160715
.
14.
Neelamani
,
S.
, and
Rajendran
,
R.
,
2002
, “
Wave Interaction With ‘’-type Breakwaters
,”
Ocean. Eng.
,
29
(
2
), pp.
151
175
.
15.
Neelamani
,
S.
, and
Rajendran
,
R.
,
2002
, “
Wave Interaction With ‘⊥’-type Breakwaters
,”
Ocean. Eng.
,
29
(
5
), pp.
561
589
.
16.
Neelamani
,
S.
, and
Vedagiri
,
M.
,
2002
, “
Wave Interaction With Partially Immersed Twin Vertical Barriers
,”
Ocean. Eng.
,
29
(
2
), pp.
215
238
.
17.
Qiao
,
W.
,
Wang
,
K. H.
, and
Sun
,
Y.
,
2018
, “
Scattering of Water Waves by a Floating Body With Two Vertically Attached Porous Walls
,”
J. Eng. Mech.
,
144
(
2
), p.
04017162
.
18.
Venkateswarlu
,
V.
, and
Karmakar
,
D.
,
2020
, “
Wave Transformation Due to Barrier-Rock Porous Structure Placed on Step-Bottom
,”
Ships and Offshore Struct.
,
15
(
8
), pp.
895
909
.
19.
Meylan
,
M. H.
, and
Squire
,
V. A.
,
1996
, “
Response of a Circular Ice Floe to Ocean Waves
,”
J. Geophys. Res. Oceans.
,
101
(
C4
), pp.
8869
8884
.
20.
Sahoo
,
T.
,
Yip
,
T. L.
, and
Chwang
,
A. T.
,
2001
, “
Scattering of Surface Waves by a Semi-Infinite Floating Elastic Plate
,”
Phys. Fluids.
,
13
(
11
), pp.
3215
3222
.
21.
Kyoung
,
J. H.
,
Hong
,
S. Y.
,
Kim
,
B. W.
, and
Cho
,
S. K.
,
2005
, “
Hydroelastic Response of a Very Large Floating Structure Over a Variable Bottom Topography
,”
Ocean. Eng.
,
32
(
17–18
), pp.
2040
2052
.
22.
Kaur
,
A.
, and
Martha
,
S. C.
,
2022
, “
Interaction of Surface Water Waves With an Elastic Plate Over an Arbitrary Bottom Topography
,”
Arch. Appl. Mech.
,
92
(
11
), pp.
1
19
.
23.
Chen
,
X. U.
,
Wu
,
Y. S.
,
Cui
,
W. C.
, and
Jensen
,
J. J.
,
2006
, “
Review of Hydroelasticity Theories for Global Response of Marine Structures
,”
Ocean. Eng.
,
33
(
3–4
), pp.
439
457
.
24.
Wang
,
C. M.
,
Tay
,
Z. Y.
,
Takagi
,
K.
, and
Utsunomiya
,
T.
,
2010
, “
Literature Review of Methods for Mitigating Hydroelastic Response of VLFS Under Wave Action
,”
ASME Appl. Mech. Rev.
,
63
(
3
), p.
030802
.
25.
Nguyen
,
H. P.
,
Dai
,
J.
,
Wang
,
C. M.
,
Ang
,
K. K.
, and
Luong
,
V. H.
,
2018
, “
Reducing Hydroelastic Responses of Pontoon-Type VLFS Using Vertical Elastic Mooring Lines
,”
Mar. Struct.
,
59
, pp.
251
270
.
26.
Singla
,
S.
,
Martha
,
S. C.
, and
Sahoo
,
T.
,
2018
, “
Mitigation of Structural Responses of a Very Large Floating Structure in the Presence of Vertical Porous Barrier
,”
Ocean. Eng.
,
165
, pp.
505
527
.
27.
Saha
,
S.
,
Mohanty
,
S. K.
, and
Bora
,
S. N.
,
2022
, “
Flexural Gravity Wave Resonance in the Presence of Current
,”
J. Waterway, Port, Coastal, and Ocean Eng.
,
148
(
3
), p.
04022003
.
28.
Singla
,
S.
,
Behera
,
H.
,
Martha
,
S. C.
, and
Sahoo
,
T.
,
2022
, “
Scattering of Water Waves by Very Large Floating Structure in the Presence of a Porous Box
,”
ASME J. Offshore. Mech. Arct. Eng.
,
144
(
4
), p.
041904
.
29.
Dalrymple
,
R. A.
,
Losada
,
M. A.
, and
Martin
,
P.
,
1991
, “
Reflection and Transmission From Porous Structures Under Oblique Wave Attack
,”
J. Fluid. Mech.
,
224
, pp.
625
644
.
30.
Sahoo
,
G.
,
Singla
,
S.
, and
Martha
,
S. C.
,
2022
, “
Scattering of Oblique Water Waves by Thick Porous Structure and Thin Elastic Plate
,”
Ocean. Eng.
,
248
, p.
110526
.
31.
Hermans
,
A.
,
2003
, “
Interaction of Free-Surface Waves With a Floating Dock
,”
J. Eng. Math.
,
45
(
1
), pp.
39
53
.
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