Abstract

Surface gravity wave interaction of composite wavy porous plate is studied by developing a numerical model using the boundary element method in the context of two-dimensional linear potential theory. Bragg scattering phenomenon is studied by considering the linearized pressure drop condition known as Darcy’s law passing through the porous structure. Numerical results are obtained through the boundary element method for the special limiting case of the existing previous literature to authenticate the accuracy of the numerical solution. The influence of wave and structural design parameters such as the number of ripple wavelengths of the wavy plate, relative plate length, structural porosities, and relative submergence depth on hydrodynamics properties such as reflection, transmission, horizontal wave load, and vertical wave coefficients are discussed. The study results of composite wavy porous plate indicate improved hydrodynamic performance as compared to the horizontal porous plate and wavy porous plate. This study is significant for practical applications in coastal engineering environments.

References

1.
Heins
,
A. E.
,
1950
, “
Water Waves Over a Channel of Finite Depth With a Submerged Plane Barrier
,”
Can. J. Math.
,
2
, pp.
210
222
.
2.
Burke
,
J.
,
1964
, “
Scattering of Surface Waves on an Infinitely Deep Fluid
,”
J. Math. Phys.
,
5
(
6
), pp.
805
819
.
3.
Siew
,
P.
, and
Hurley
,
D.
,
1977
, “
Long Surface Waves Incident on a Submerged Horizontal Plate
,”
J. Fluid Mech.
,
83
(
1
), pp.
141
151
.
4.
Patarapanich
,
M.
,
1984
, “
Maximum and Zero Reflection From Submerged Plate
,”
J. Waterw. Port Coastal Ocean Eng.
,
110
(
2
), pp.
171
181
.
5.
Patarapanich
,
M.
,
1984
, “
Forces and Moment on a Horizontal Plate Due to Wave Scattering
,”
Coastal Eng.
,
8
(
3
), pp.
279
301
.
6.
Yu
,
X.
,
2002
, “
Functional Performance of a Submerged and Essentially Horizontal Plate for Offshore Wave Control: A Review
,”
Coastal Eng. J.
,
44
(
02
), pp.
127
147
.
7.
Neelamani
,
S.
, and
Reddy
,
M.
,
1992
, “
Wave Transmission and Reflection Characteristics of a Rigid Surface and Submerged Horizontal Plate
,”
Ocean Eng.
,
19
(
4
), pp.
327
341
.
8.
Yu
,
X.
, and
Chwang
,
A. T.
,
1994
, “
Water Waves Above Submerged Porous Plate
,”
J. Eng. Mech.
,
120
(
6
), pp.
1270
1282
.
9.
Cho
,
I.
, and
Kim
,
M.
,
2013
, “
Transmission of Oblique Incident Waves by a Submerged Horizontal Porous Plate
,”
Ocean Eng.
,
61
, pp.
56
65
.
10.
Usha
,
R.
, and
Gayathri
,
T.
,
2005
, “
Wave Motion Over a Twin-Plate Breakwater
,”
Ocean Eng.
,
32
(
8–9
), pp.
1054
1072
.
11.
Neelamani
,
S.
, and
Gayathri
,
T.
,
2006
, “
Wave Interaction With Twin Plate Wave Barrier
,”
Ocean Eng.
,
33
(
3–4
), pp.
495
516
.
12.
Cho
,
I.
,
Koh
,
H.
,
Kim
,
J.
, and
Kim
,
M.
,
2013
, “
Wave Scattering by Dual Submerged Horizontal Porous Plates
,”
Ocean Eng.
,
73
, pp.
149
158
.
13.
Liang
,
H.
,
Zheng
,
S.
,
Shao
,
Y.
,
Chua
,
K. H.
,
Choo
,
Y. S.
, and
Greaves
,
D.
,
2021
, “
Water Wave Scattering by Impermeable and Perforated Plates
,”
Phys. Fluids
,
33
(
7
), p.
077111
.
14.
Mohapatra
,
S.
, and
Soares
,
C. G.
,
2021
, “
Surface Gravity Wave Interaction With a Horizontal Flexible Floating Plate and Submerged Flexible Porous Plate
,”
Ocean Eng.
,
237
, p.
109621
.
15.
Davies
,
A.
, and
Heathershaw
,
A.
,
1984
, “
Surface-Wave Propagation Over Sinusoidally Varying Topography
,”
J. Fluid Mech.
,
144
, pp.
419
443
.
16.
O’Hare
,
T. J.
, and
Davies
,
A.
,
1992
, “
A New Model for Surface Wave Propagation Over Undulating Topography
,”
Coastal Eng.
,
18
(
3–4
), pp.
251
266
.
17.
Suh
,
K. D.
,
Lee
,
C.
, and
Park
,
W. S.
,
1997
, “
Time-Dependent Equations for Wave Propagation on Rapidly Varying Topography
,”
Coastal Eng.
,
32
(
2–3
), pp.
91
117
.
18.
Kirby
,
J. T.
, and
Anton
,
J. P.
,
1991
, “Bragg Reflection of Waves by Artificial Bars,”
Coastal Engineering 1990
, pp.
757
768
.
19.
Guazzelli
,
E.
,
Rey
,
V.
, and
Belzons
,
M.
,
1992
, “
Higher-Order Bragg Reflection of Gravity Surface Waves by Periodic Beds
,”
J. Fluid Mech.
,
245
, pp.
301
317
.
20.
Cho
,
Y.-S.
,
2000
, “
Bragg Resonant Reflection of Obliquely Incident Water Waves
,”
Water Eng. Res.
,
1
(
1
), pp.
75
81
.
21.
Parsons
,
N.
, and
Martin
,
P.
,
1994
, “
Scattering of Water Waves by Submerged Curved Plates and by Surface-Piercing Flat Plates
,”
Appl. Ocean Res.
,
16
(
3
), pp.
129
139
.
22.
Chwang
,
A. T.
, and
Wu
,
J.
,
1994
, “
Wave Scattering by Submerged Porous Disk
,”
J. Eng. Mech.
,
120
(
12
), pp.
2575
2587
.
23.
Jeon
,
C.-H.
, and
Cho
,
Y.-S.
,
2006
, “
Bragg Reflection of Sinusoidal Waves Due to Trapezoidal Submerged Breakwaters
,”
Ocean Eng.
,
33
(
14–15
), pp.
2067
2082
.
24.
Medina-Rodríguez
,
A.
,
Bautista
,
E.
, and
Méndez
,
F.
,
2016
, “
Asymptotic Analysis of the Interaction Between Linear Long Waves and a Submerged Floating Breakwater of Wavy Surfaces
,”
Appl. Ocean Res.
,
59
, pp.
345
365
.
25.
Kar
,
P.
,
Koley
,
S.
, and
Sahoo
,
T.
,
2020
, “
Bragg Scattering of Long Waves by an Array of Trenches
,”
Ocean Eng.
,
198
, p.
107004
.
26.
Li
,
A.-J.
,
Liu
,
Y.
,
Liu
,
X.
, and
Zhao
,
Y.
,
2020
, “
Analytical and Experimental Studies on Bragg Scattering of Water Waves by Multiple Submerged Perforated Semi-Circular Breakwaters
,”
Ocean Eng.
,
209
, p.
107419
.
27.
Liu
,
W.
,
Liu
,
Y.
, and
Zhao
,
X.
,
2019
, “
Numerical Study of Bragg Reflection of Regular Water Waves Over Fringing Reefs Based on a Boussinesq Model
,”
Ocean Eng.
,
190
, p.
106415
.
28.
Yueh
,
C.-Y.
,
Chuang
,
S.-H.
, and
Wen
,
C.-C.
,
2016
, “
Wave Scattering by Submerged Composite Wavy Plate Breakwaters Using a Dual BEM
,”
Ocean Eng.
,
124
, pp.
192
203
.
29.
Mohapatra
,
A.
,
Vijay
,
K.
, and
Sahoo
,
T.
,
2021
, “
Bragg Scattering of Surface Gravity Waves by a Submerged Wavy Porous Plate
,”
Ocean Eng.
,
219
, p.
108273
.
30.
Vijay
,
K.
,
He
,
S.
,
Zhao
,
Y.
,
Liu
,
Y.
, and
Sahoo
,
T.
,
2020
, “
Gravity Wave Interaction With a Submerged Wavy Porous Plate
,”
Ships Offshore Struct.
,
15
(
sup1
), pp.
S123
S133
.
31.
Vijay
,
K.
,
Nishad
,
C. S.
,
Neelamani
,
S.
, and
Sahoo
,
T.
,
2021
, “
Wave Interaction With Multiple Wavy Porous Barriers Using Dual Boundary Element Method
,”
Eng. Anal. Boundary Elem.
,
122
, pp.
176
189
.
32.
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2015
, “
Wave Forces on a Submerged Horizontal Plate-Part I: Theory and Modelling
,”
J. Fluids Struct.
,
54
, pp.
566
579
.
33.
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2015
, “
Wave Forces on a Submerged Horizontal Plate-Part II: Solitary and Cnoidal Waves
,”
J. Fluids Struct.
,
54
, pp.
580
596
.
34.
Hayatdavoodi
,
M.
,
Chen
,
Y.
,
Zhao
,
B.
, and
Ertekin
,
R. C.
,
2023
, “
Experiments and Computations of Wave-Induced Oscillations of Submerged Horizontal Plates
,”
Phys. Fluids
,
35
(
1
), p.
017121
.
35.
Hayatdavoodi
,
M.
,
Treichel
,
K.
, and
Ertekin
,
R. C.
,
2019
, “
Parametric Study of Nonlinear Wave Loads on Submerged Decks in Shallow Water
,”
J. Fluids Struct.
,
86
, pp.
266
289
.
36.
Mohapatra
,
A. K.
, and
Sahoo
,
T.
,
2022
, “
Surface Gravity Wave Interaction With a Submerged Composite Wavy Porous Plate Attached to a Vertical Wall
,”
ASME J. Offshore Mech. Arct. Eng.
,
144
(
1
), p.
011904
.
37.
Singla
,
S.
,
Sahoo
,
T.
,
Martha
,
S.
, 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
.
38.
Katsikadelis
,
J. T.
,
2002
,
Boundary Elements: Theory and Applications
,
Elsevier
,
Oxford, UK
.
39.
Nishad
,
C. S.
,
Chandra
,
A.
, and
Sekhar
,
G. R.
,
2016
, “
Flows in Slip-Patterned Micro-Channels Using Boundary Element Methods
,”
Eng. Anal. Boundary Elem.
,
73
, pp.
95
102
.
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