Physical experiments are conducted to study the interaction between a solitary wave and a finite horizontal plate submerged at a depth equal to 1/4 of the water depth. The spatial and temporal variation of the three-dimensional (3D) surface deformation is measured using a multi-lens stereo reconstruction system. The hydrodynamic loads are measured by underwater load cells. The plate-induced shoaling causes 3D wave focusing, leading to an increased maximum elevation along the streamwise centerline of the plate. The detailed wave focusing process and the influence of wave amplitude on focusing are presented based on the results obtained through image processing. The characteristics of the horizontal forces, vertical forces, and pitching moments are discussed. A 6-stage loading process based on the maxima of vertical wave force and pitching moment is proposed. It is coupled with the synchronous surface deformation to reveal the loading mechanism. It proves that the vertical wave force on the plate reduces apparently compared with the results from 2D experiments. The surface elevation and wave-induced load data provide an excellent benchmark for further studies on the 3D nonlinear interaction between a solitary wave and a submerged plate.

1.
P. L.-F.
Liu
and
Y.
Cheng
, “
A numerical study of the evolution of a solitary wave over a shelf
,”
Phys. Fluids
13
(
6
),
1660
1667
(
2001
).
2.
W.
Craig
,
P.
Guyenne
,
J.
Hammack
,
D.
Henderson
, and
C.
Sulem
, “
Solitary water wave interactions
,”
Phys. Fluids
18
(
5
),
057106
(
2006
).
3.
G. K.
Pedersen
,
E.
Lindstrøm
,
A. F.
Bertelsen
,
A.
Jensen
,
D.
Laskovski
, and
G.
Sælevik
, “
Runup and boundary layers on sloping beaches
,”
Phys. Fluids
25
(
1
),
012102
(
2013
).
4.
S.-C.
Hsiao
and
T.-C.
Lin
, “
Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and RANS modeling
,”
Coast. Eng.
57
(
1
),
1
18
(
2010
).
5.
V.
Rey
,
J.
Charland
, and
J.
Touboul
, “
Wave-current interaction in the presence of a three-dimensional bathymetry: Deep water wave focusing in opposing current conditions
,”
Phys. Fluids
26
(
9
),
096601
(
2014
).
6.
C.-M.
Hsieh
,
A.
Sau
,
R. R.
Hwang
, and
W. C.
Yang
, “
Nonlinear interaction and wave breaking with a submerged porous structure
,”
Phys. Fluids
28
(
12
),
126601
(
2016
).
7.
Y.
Cheng
,
G.
Li
,
C.
Ji
, and
G.
Zhai
, “
Numerical investigation of solitary wave slamming on an oscillating wave surge converter
,”
Phys. Fluids
31
(
3
),
037102
(
2019
).
8.
X.
Yu
, “
Functional performance of a submerged and essentially horizontal plate for offshore wave control: A review
,”
Coast. Eng. J.
44
(
02
),
127
147
(
2002
).
9.
M.
Patarapanich
, “
Forces and moment on a horizontal plate due to wave scattering
,”
Coast. Eng.
8
(
3
),
279
301
(
1984
).
10.
H.
Kojima
,
A.
Yoshida
, and
T.
Nakamura
, “
Linear and nonlinear wave forces exerted on a submerged horizontal plate
,”
Proc. of 24th Intern. Conf. on Coast. Eng.
1994
,
1312
1326
(
1995
).
11.
M.
Hayatdavoodi
and
R. C.
Ertekin
, “
Wave forces on a submerged horizontal plate—Part II: Solitary and cnoidal waves
,”
J. Fluid Struct.
54
,
580
596
(
2015
).
12.
G.
Kulin
,
Solitary Wave Forces on Submerged Cylinders and Plates
(
U.S. Department of Commerce; National Bureau of Standards
,
1958
).
13.
J. A.
French
, “
Wave uplift pressures on horizontal platforms
,” Ph.D. dissertation (
California Institute of Technology
,
Pasadena, CA
,
1970
).
14.
B.
Seiffert
,
M.
Hayatdavoodi
, and
R. C.
Ertekin
, “
Experiments and computations of solitary-wave forces on a coastal-bridge deck. Part I: Flat plate
,”
Coast. Eng.
88
,
194
209
(
2014
).
15.
M.
Hayatdavoodi
and
R. C.
Ertekin
, “
Review of wave loads on coastal bridge decks
,”
Appl. Mech. Rev.
68
(
3
),
030802
(
2016
).
16.
J.
Dong
,
B.
Wang
, and
H.
Liu
, “
Wave forces on a submerged horizontal plate over a sloping beach due to a solitary wave
,” in
Proceedings of 12th Pacific-Asia Offshore Mechanics Symposium
(
Gold Coast
,
Australia
,
2016
), pp.
386
392
.
17.
C.
Liu
,
Z.
Huang
, and
S. K.
Tan
, “
Nonlinear scattering of non-breaking waves by a submerged horizontal plate: Experiments and simulations
,”
Ocean Eng.
36
(
17-18
),
1332
1345
(
2009
).
18.
H. Y.
Lo
and
P. L. F.
Liu
, “
Solitary waves incident on a submerged horizontal plate
,”
J. Waterw. Port, Coast., Ocean Eng.
140
(
3
),
04014009
(
2013
).
19.
M.
Hayatdavoodi
,
R. C.
Ertekin
, and
B. D.
Valentine
, “
Solitary and cnoidal wave scattering by a submerged horizontal plate in shallow water
,”
AIP Adv.
7
(
6
),
065212
(
2017
).
20.
G.
Pedersen
and
B.
Gjevik
, “
Run-up of solitary waves
,”
J. Fluid Mech.
135
,
283
299
(
1983
).
21.
J.
Chase
and
L. J.
Cote
, “
The directional spectrum of a wind generated sea as determined from data obtained by the Stereo Wave Observation Project
,”
Tech. Rep., Department of Meteorology and Oceanography and Engineering Statistics Group; New York University
,
1957
, p.
267
.
22.
Y.
Sugimori
, “
A study of the application of the holographic method to the determination of the directional spectrum of ocean waves
,”
Deep-Sea Res. Oceanogr. Abstr.
22
(
5
),
339
350
(
1975
).
23.
L. H.
Holthuijsen
, “
Observations of the directional distribution of ocean-wave energy in fetch-limited conditions
,”
J. Phys. Oceanogr.
13
(
2
),
191
207
(
1983
).
24.
K. T.
Holland
,
R. A.
Holman
,
T. C.
Lippmann
,
J.
Stanley
, and
N.
Plant
, “
Practical use of video imagery in nearshore oceanographic field studies
,”
IEEE J. Ocean. Eng.
22
(
1
),
81
92
(
1997
).
25.
Z.
Zhang
, “
A flexible new technique for camera calibration
,”
IEEE Trans. Pattern Anal. Mach. Intell.
22
(
11
),
1330
1334
(
2000
).
26.
R.
Holman
and
M. C.
Haller
, “
Remote sensing of the nearshore
,”
Annu. Rev. Mar. Sci
5
,
95
113
(
2013
).
27.
L.
Gui
,
H.
Yoon
, and
F.
Stern
, “
Techniques for measuring bulge–scar pattern of free surface deformation and related velocity distribution in shallow water flow over a bump
,”
Exp. Fluids
55
(
4
),
1721
(
2014
).
28.
A. J.
Campbell
,
A. J.
Bechle
, and
C. H.
Wu
, “
Observations of surface waves interacting with ice using stereo imaging
,”
J. Geophys. Res.: Oceans.
119
(
6
),
3266
3284
, (
2014
).
29.
A. J.
Bechle
and
C. H.
Wu
, “
Virtual wave gauges based upon stereo imaging for measuring surface wave characteristics
,”
Coast. Eng.
58
(
4
),
305
316
(
2011
).
30.
L.
Chatellier
,
S.
Jarny
,
F.
Gibouin
, and
L.
David
, “
A parametric PIV/DIC method for the measurement of free surface flows
,”
Exp. Fluids
54
(
3
),
1488
(
2013
).
31.
G.
Gomit
,
L.
Chatellier
,
D.
Calluaud
,
L.
David
,
D.
Fréchou
,
R.
Boucheron
,
O.
Perelman
, and
C.
Hubert
, “
Large-scale free surface measurement for the analysis of ship waves in a towing tank
,”
Exp. Fluids
56
(
10
),
184
(
2015
).
32.
A.
Chabchoub
,
K.
Mozumi
,
N.
Hoffmann
 et al, “
Directional soliton and breather beams
,”
Proc. Natl. Acad. Sci. U. S. A.
116
(
20
),
9759
9763
(
2019
).
33.
Y.
Watanabe
,
Y.
Mitobe
, and
K.
Oshima
, “
An imaging technique for measuring wave surface shapes
,”
Coast. Eng. J.
53
(
04
),
549
565
(
2011
).
34.
F.
Evers
and
W. H.
Hager
, “
Videometric water surface tracking: Towards investigating spatial impulse waves
,” in
36th IAHR World Congress: Deltas of the Future and What Happens Upstream
(
ETH-Zürich
,
2015
).
35.
A.
Benetazzo
, “
Measurements of short water waves using stereo matched image sequences
,”
Coast. Eng.
53
(
12
),
1013
1032
(
2006
).
36.
M. H.
Meylan
,
L. G.
Bennetts
,
C.
Cavaliere
,
A.
Alberello
, and
A.
Toffoli
, “
Experimental and theoretical models of wave-induced flexure of a sea ice floe
,”
Phys. Fluids
27
(
4
),
041704
(
2015
).
37.
S.
Vries
,
D. F.
Hill
,
M. A.
De Schipper
, and
M. J. F.
Stive
, “
Remote sensing of surf zone waves using stereo imaging
,”
Coast. Eng.
58
(
3
),
239
250
(
2011
).
38.
D.
Astruc
,
S.
Cazin
,
E.
Cid
 et al, “
A stereoscopic method for rapid monitoring of the spatio-temporal evolution of the sand-bed elevation in the swash zone
,”
Coast. Eng.
60
,
11
20
(
2012
).
39.
L.
Lacaze
,
A.
Paci
,
E.
Cid
,
S.
Cazin
,
O.
Eiff
,
J. G.
Esler
, and
E. R.
Johnson
, “
Wave patterns generated by an axisymmetric obstacle in a two-layer flow
,”
Exp. Fluids
54
(
12
),
1618
(
2013
).
40.
H.
Yeh
,
H.
Ko
,
J.
Knowles
, and
S.
HarRy
, “
Solitary waves perturbed by a broad sill. Part 2. Propagation along the sill
,”
J. Fluid Mech.
883
,
A26
(
2020
).
41.
Q.
Wang
,
Y.-L.
Fang
, and
H.
Liu
, “
Physical generation of Tsunami waves in offshore region
,”
J. Earthquake Tsunami
12
(
02
),
1840003
(
2018
).
42.
R.
Grimshaw
, “
The solitary wave in water of variable depth. Part 2
,”
J. Fluid Mech.
46
(
3
),
611
622
(
1971
).
43.
S.
Malek-Mohammadi
and
F. Y.
Testik
, “
New methodology for laboratory generation of solitary waves
,”
J. Waterw. Port Coast. Ocean Eng.
136
(
5
),
286
294
(
2010
).
44.
D. G.
Goring
, “
Tsunamis—The propagation of long waves onto a shelf
,” Ph.D. dissertation (
California Institute of Technology
,
Pasadena, CA
,
1978
).
45.
Q.
Wang
,
Y.
Fang
, and
H.
Liu
, “
An experimental study on wave loads on a submerged horizontal plate in solitary wave
,” in
The 29th International Ocean and Polar Engineering Conference
(
ISOPE
,
Hawaii
,
USA
,
2019
).
46.
Q.
Wang
,
Y.-l.
Fang
, and
H.
Liu
, “
Multi-lens stereo reconstruction of wave surface in a wave basin
,”
J. Hydrodyn.
31
(
5
),
1069
1072
(
2019
).
47.
J. M.
Wanek
and
C. H.
Wu
, “
Automated trinocular stereo imaging system for three-dimensional surface wave measurements
,”
Ocean Eng.
33
(
5-6
),
723
747
(
2006
).
48.
J.
Dong
, “
A two-dimensional study of wave loadings on a submerged horizontal plate over variable topography
,” Ph.D. dissertation (
Shanghai Jiao Tong University
,
2017
).
You do not currently have access to this content.