Abstract

This paper is concerned with scattering of an obliquely incident surface water wave train by an obstacle in the form of a thick horizontal barrier of rectangular cross section present in finite depth water. Four different geometrical configurations of the obstacle are considered. It may be surface-piercing or bottom-standing, or in the form of a submerged block not extending down to the bottom, or in the form of a thick wall with a submerged gap. Multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving first-kind integral equations are utilized in the mathematical analysis to obtain very accurate numerical estimates for the reflection coefficient, which are depicted graphically against the wave number for each configurations of the thick barrier. [S0892-7219(00)00701-9]

Issue Section:
Technical Papers
Keywords:
water waves, surface waves (fluid), Galerkin method, integral equations, scattering
Topics:
Galerkin method, Integral equations, Reflectance, Scattering (Physics), Water waves, Waves, Water, Polynomials, Fluids, Trains
1.
Ursell
,
F.
,
1947
, “
The Effect of a Fixed Vertical Barrier on Surface Waves in Deep Water
,”
Proc. Camb. Phil. Soc.
,
43
, pp.
374
–
382
.
2.
Levine, H., and Rodemich, E., 1958, “Scattering of Surface Waves on an Ideal Fluid,” Math. Stat. Lab. Tech. Rep., 78, Standard University.
3.
Williams
,
W. E.
,
1966
, “
Note on the Scattering of Water Waves by a Vertical Barrier
,”
Proc. Camb. Phil. Soc.
,
62
, pp.
507
–
509
.
4.
Evans
,
D. V.
,
1970
, “
Diffraction of Surface Waves by a Submerged Vertical Plate
,”
J. Fluid Mech.
,
40
, pp.
433
–
451
.
5.
Porter
,
D.
,
1972
, “
The Transmission of Surface Waves Through a Gap in a Vertical Barrier
,”
Proc. Camb. Phil. Soc.
,
71
, pp.
411
–
421
.
6.
Banerjea
,
S.
,
1996
, “
Scattering of Water Waves by a Vertical Wall With Gaps
,”
J. Austral. Math. Soc. Ser. B
,
37
, pp.
512
–
529
.
7.
Evans
,
D. V.
, and
Morris
,
C. A. N.
,
1972
, “
The Effect of a Fixed Vertical Barrier on Obliquely Incident Surface Waves in Deep Water
,”
J. Inst. Math. Appl.
,
9
, pp.
198
–
204
.
8.
Packham
,
B. A.
, and
Williams
,
W. E.
,
1972
, “
A Note on the Transmission of Water Waves Through Small Aperatures
,”
J. Inst. Math. Appl.
,
10
, pp.
176
–
184
.
9.
Losada
,
I. J.
,
Losada
,
M. S.
, and
Roldan
,
A. J.
,
1992
, “
Propagation of Oblique Incident Waves Past Rigid Vertical Thin Barriers
,”
Appl. Ocean Res.
,
14
, pp.
191
–
199
.
10.
Mandal
,
B. N.
, and
Dolai
,
D. P.
,
1994
, “
Oblique Water Waves Diffraction by Thin Vertical Barriers in Water of Uniform Finite Depth
,”
Appl. Ocean Res.
,
16
, pp.
195
–
203
.
11.
Porter
,
R.
, and
Evans
,
D. V.
,
1995
, “
Complimentary Approximations to Wave Scattering by Vertical Barriers
,”
J. Fluid Mech.
,
294
, pp.
155
–
180
.
12.
Mandal
,
B. N.
, and
Das
,
P.
,
1996
, “
Oblique Diffraction of Surface Waves by a Submerged Vertical Plate
,”
J. Eng. Math.
,
30
, pp.
459
–
470
.
13.
Mei
,
C. C.
, and
Black
,
J. L.
,
1969
, “
Scattering of Surface Waves by Rectangular Obstacles in Waters of Finite Depth
,”
J. Fluid Mech.
,
38
, pp.
499
–
511
.
14.
Bai
,
K. J.
,
1975
, “
Diffraction of Oblique Waves by an Infinite Cylinder
,”
J. Fluid Mech.
,
68
, pp.
513
–
535
.
15.
Liu
,
P. L.-F.
, and
Wu
,
T.
,
1987
, “
Wave Transmission Through Submerged Apertures
,”
J. Wtry., Port, Coastal Ocean Engng.
,
113
, pp.
660
–
671
.
16.
Dingemans, M. W., 1997, “Water Wave Propagation over Uneven Bottoms,” Adv. Series on Ocean Eng., 13, World Scientific, pp. 138–141.
17.
Kanoria
,
M.
,
Dolai
,
D. P.
, and
Mandal
,
B. N.
,
1999
, “
Water Waves Scattering by Thick Vertical Barriers
,”
J. Eng. Math.
,
35
, pp.
361
–
384
.
18.
Evans
,
D. V.
, and
Fernyhough
,
M.
,
1995
, “
Edge Waves Along Periodic Coastlines—Part 2
,”
J. Fluid Mech.
,
297
, pp.
307
–
325
.
19.
Nadaoka, K., and Nakagawa, Y., 1991, “A Galerkin Derivation of Fully Dispersive Wave Equations and its Background,” Dept. of Civil Engng., Tokyo Inst. of Tech., Tech. Rep., 44, pp. 63–75 (in Japanese).
20.
Nadaoka
,
K.
,
Bejiand
,
S.
, and
Nakagawa
,
Y.
,
1997
, “
A Fully Despersive Weakly Nonlinear Model for Water Waves
,”
Proc. R. Soc. London, Ser. A
,
453
, pp.
303
–
318
.
21.
Martin
,
P. A.
, and
Dalrymple
,
R. A.
,
1988
, “
Scattering of Long Waves by Cylindrical Obstacles and Gratings Using Matched Asymptotic Expansions
,”
J. Fluid Mech.
,
188
, pp.
465
–
490
.
22.
McIver, P., 1994, “Low-Frequency Asymptotics of Hydrodynamic Forces on Fixed and Floating Structures,” Ocean Wave Engineering, ed., M. Rahman, Computational Mechanics Publications, U.K., pp. 1–49.
Copyright © 2000
 by ASME
You do not currently have access to this content.