We present a comparative study of the two-dimensional linear and nonlinear vertical and horizontal wave forces and overturning moment due to the unsteady flow of an inviscid, incompressible fluid over a fully submerged horizontal, fixed deck in shallow-water. The problem is approached on the basis of the level I Green–Naghdi (G–N) theory of shallow-water waves. The main objective of this paper is to present a comparison of the solitary and periodic wave loads calculated by use of the G–N equations, with those computed by the Euler equations and the existing laboratory measurements, and also with linear solutions of the problem for small-amplitude waves. The results show a remarkable similarity between the G–N and the Euler solutions and the laboratory measurements. In particular, the calculations predict that the thickness of the deck, if it is not “too thick,” has no effect on the vertical forces and has only a slight influence on the two-dimensional horizontal positive force. The calculations also predict that viscosity of the fluid has a small effect on these loads. The results have applications to various physical problems such as wave forces on submerged coastal bridges and submerged breakwaters.

References

References
1.
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2012
, “
Nonlinear Forces on a Submerged, Horizontal Plate: The GN Theory
,”
The 27th International Workshop on Water Waves and Floating Bodies
, Copenhagen, Denmark, Apr. 22–25, pp.
69
72
.
2.
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2014
, “
Wave Forces on a Submerged Horizontal Plate. Part I: Theory and Modeling
,”
J. Fluids Struct
(in press).
3.
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2014
, “
Wave Forces on a Submerged Horizontal Plate. Part II: Solitary and Cnoidal Waves
,”
J. Fluids Struct
(in press).
4.
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2014
, “
A Comparative Study of Nonlinear Shallow-Water Wave Loads on a Submerged Horizontal Box
,”
Proceedings of 33rd ASME International Conference on Ocean, Offshore and Arctic Engineering
,
ASME
Paper No. OMAE2014-24572. 10.1115/OMAE2014-24572
5.
Green
,
A. E.
, and
Naghdi
,
P. M.
,
1974
, “
On the Theory of Water Waves
,”
Proc. R. Soc. London, Ser. A
,
338
(
1612
), pp.
43
55
.10.1098/rspa.1974.0072
6.
Green
,
A. E.
, and
Naghdi
,
P. M.
,
1976
, “
Directed Fluid Sheets
,”
Proc. R. Soc. London, Ser. A
,
347
(
1651
), pp.
447
473
.10.1098/rspa.1976.0011
7.
Green
,
A. E.
, and
Naghdi
,
P. M.
,
1976
, “
A Derivation of Equations for Wave Propagation in Water of Variable Depth
,”
J. Fluid Mech.
,
78
(
10
), pp.
237
246
.10.1017/S0022112076002425
8.
Ertekin
,
R. C.
,
Webster
,
W. C.
, and
Wehausen
,
J. V.
,
1986
, “
Waves Caused by a Moving Disturbance in a Shallow Channel of Finite Width
,”
J. Fluid Mech.
,
169
(
7
), pp.
275
292
.10.1017/S0022112086000630
9.
Shields
,
J. J.
, and
Webster
,
W. C.
,
1988
, “
On Direct Methods in Water-Wave Theory
,”
J. Fluid Mech.
,
197
, pp.
171
199
.10.1017/S0022112088003222
10.
Ertekin
,
R. C.
, and
Becker
,
J. M.
,
1998
, “
Nonlinear Diffraction of Waves by a Submerged Shelf in Shallow Water
,”
ASME J. Offshore Mech. Arct. Eng.
,
120
(4), pp.
212
220
.10.1115/1.2829542
11.
Zhao
,
B.
,
Duan
,
W.
, and
Ertekin
,
R.
,
2014
, “
Application of Higher-Level GN Theory to Some Wave Transformation Problems
,”
Coastal Eng.
,
83
, pp.
177
189
.10.1016/j.coastaleng.2013.10.010
12.
Ertekin
,
R. C.
, and
Xia
,
D.
,
2014
, “
Hydroelastic Response of a Floating Runway to Cnoidal Waves
,”
Phys. Fluids
,
26
(
2
), p.
027101
.10.1063/1.4862916
13.
Seiffert
,
B.
,
Hayatdavoodi
,
M.
, and
Ertekin
,
R. C.
,
2014
, “
Experiments and Computations of Solitary-Wave Forces on a Coastal-Bridge Deck. Part I: Flat Plate
,”
Coastal Eng.
,
88
, pp.
194
209
.10.1016/j.coastaleng.2014.01.005
14.
Hayatdavoodi
,
M.
,
Seiffert
,
B.
, and
Ertekin
,
R. C.
,
2014
, “
Experiments and Computations of Solitary-Wave Forces on a Coastal-Bridge Deck. Part II: Deck With Girders
,”
Coastal Eng.
,
88
, pp.
210
228
.10.1016/j.coastaleng.2014.02.007
15.
Siew
,
P. F.
, and
Hurley
,
D. G.
,
1977
, “
Long Surface Waves Incident on a Submerged Horizontal Plate
,”
J. Fluid Mech.
,
83
(
10
), pp.
141
151
.10.1017/S0022112077001098
16.
HYDRAN,
2012
, “
A Computer Program for the Hydroelastic Response Analysis of Ocean Structures
,” Version 5.1.7, Offcoast Inc., Kailua, HI.
17.
Ertekin
,
R. C.
,
Riggs
,
H. R.
,
Che
,
X. L.
, and
Du
,
S. X.
,
1993
, “
Efficient Methods for Hydroelastic Analysis of Very Large Floating Structures
,”
J. Ship Res.
,
37
(
1
), pp.
58
76
.
18.
Riggs
,
H. R.
,
Ertekin
,
R. C.
, and
Mills
,
T.
,
1999
, “
Impact of Stiffness on the Response of a Multimodule Mobile Offshore Base
,”
Int. J. Offshore Polar Eng.
,
9
(
2
), pp.
126
133
.
19.
Riggs
,
H. R.
,
Suzuki
,
H.
,
Ertekin
,
R. C.
,
Kim
,
J. W.
, and
Iijima
,
K.
,
2008
, “
Comparison of Hydroelastic Computer Codes Based on the ISSC VLFS Benchmark
,”
Ocean Eng.
,
35
(
7
), pp.
589
597
.10.1016/j.oceaneng.2008.01.012
20.
Korde
,
U. A.
, and
Ertekin
,
R.
,
2014
, “
On Wave Energy Focusing and Conversion in Open Water
,”
Renewable Energy
,
62
, pp.
84
99
.10.1016/j.renene.2013.06.033
21.
Green
,
A. E.
, and
Naghdi
,
P. M.
,
1977
, “
Water Waves in a Nonhomogeneous Incompressible Fluid
,”
ASME J. Appl. Mech.
,
44
(
4
), pp.
523
528
.10.1115/1.3424129
22.
Ertekin
,
R. C.
, and
Sundararaghavan
,
H.
,
2003
, “
Refraction and Diffraction of Nonlinear Waves in Coastal Waters by the Level I Green–Naghdi Equations
,”
Proceedings of the 22nd ASME International Conference on Offshore Mechanics and Arctic Engineering
, OMAE’03,
ASME
Paper No. OMAE2003-37323. 10.1115/OMAE2003-37323
23.
Ertekin
,
R. C.
,
1984
, “
Soliton Generation by Moving Disturbances in Shallow Water: Theory, Computation and Experiment
,” Ph. D. dissertation, University of California at Berkeley, Berkeley, CA.
24.
Naghdi
,
P. M.
, and
Rubin
,
M. B.
,
1981
, “
On Inviscid Flow in a Waterfall
,”
J. Fluid Mech.
,
103
(
1
), pp.
375
387
.10.1017/S0022112081001389
25.
Naghdi
,
P. M.
, and
Rubin
,
M. B.
,
1981
, “
On the Transition to Planning of a Boat
,”
J. Fluid Mech.
,
103
, pp.
345
374
.10.1017/S0022112081001377
26.
Hayatdavoodi
,
M.
,
2013
, “
Nonlinear Wave Loads on Decks of Coastal Structures
,” Ph. D. dissertation, University of Hawaii at Manoa, Honolulu, HI.
27.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
1992
,
Numerical Recipes in Fortran
,
2nd ed.
,
Cambridge University Press
,
UK
.
28.
Brater
,
E. F.
,
McNown
,
J. S.
, and
Stair
,
L. D.
,
1958
, “
Wave Forces on Submerged Structures
,”
ASCE J. Hydraul. Div.
,
84
, pp.
1
26
.
29.
Patarapanich
,
M.
,
1984
, “
Forces and Moment on a Horizontal Plate due to Wave Scattering
,”
Coastal Eng.
,
8
(
3
), pp.
279
301
.10.1016/0378-3839(84)90006-1
30.
Wiegel
,
R. L.
,
1964
,
Oceanographical Engineering
,
Prentice-Hall, Inc.
,
Englewood Cliffs, NJ
.
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