Generation of flexural gravity waves in a two-layer fluid due to the forced motion of a vertical rigid wavemaker is studied in both finite and infinite water depths. The two-dimensional (2D) fluid domain having an interface is covered by a semi-infinite ice sheet, which is modeled as an elastic beam. As an application of the wavemaker problem, flexural gravity wave reflection by a vertical cliff is analyzed. Under the assumptions of small amplitude water wave theory and structural response, the mathematical models are solved using a recently developed expansion formulae and the associated orthogonal mode-coupling relations as appropriate for finite and infinite water depths. Effect of three types of edges such as free edge, simply supported edge, and built-in edge on the wave reflection by the vertical cliff is analyzed whilst, for the wavemaker, the floating ice sheet is assumed to have free edge. Effect of various physical parameters on the wave motion is studied by analyzing the reflection coefficients, deflection of the ice sheet, interface elevation, strain and shear force on the floating ice sheet.

References

References
1.
Stoker
,
J. J.
,
1947
, “
Surface Waves in Water of Variable Depth
,”
Q. Appl. Math.
,
5
, pp.
1
54
.
2.
Christensen
,
F. T.
,
1987
, “
Vertical Ice Forces on Long Straight Walls
,”
Cold Reg. Sci. Technol.
,
13
(
3
), pp.
215
218
.10.1016/0165-232X(87)90001-2
3.
Williams
,
T.
, and
Squire
,
V.
,
2002
, “
Ice Coupled Waves Near a Deep Water Tide Crack or Ice Jetty. In: Ice in the Environment
,”
Proceedings of the 16th IAHR International Symposium on Ice
, Vol. 2, pp.
318
326
.
4.
Chakrabarti
,
A.
,
Ahluwalia
,
D. S.
, and
Manam
,
S. R.
,
2003
, “
Surface Water Waves Involving a Vertical Barrier in the Presence of an Ice-Cover
,”
Int. J. Eng. Sci.
,
41
(
10
), pp.
1145
1162
.10.1016/S0020-7225(02)00375-0
5.
Brocklehurst
,
P.
,
Korobkin
,
A. A.
, and
Parau
,
E. I.
,
2010
, “
Interaction of Hydro-Elastic Waves With a Vertical Wall
,”
J. Eng. Math.
,
68
(
3–4
), pp.
215
261
.10.1007/s10665-010-9386-8
6.
Bhattacharjee
,
J.
, and
Guedes Soares
,
C.
,
2012
, “
Flexural Gravity Wave Over a Floating Ice Sheet Near a Vertical Wall
,”
J. Eng. Math.
,
75
(
1
), pp.
29
48
.10.1007/s10665-011-9511-3
7.
Tkacheva
,
L. A.
,
2013
, “
Interaction of Surface and Flexural-Gravity Waves in Ice Covered With a Vertical Wall
,”
J. Appl. Mech. Tech. Phys.
,
54
(
4
), pp.
651
661
.10.1134/S0021894413040160
8.
Havelock
,
T. H.
,
1929
, “
Forced Surface Waves on Water
,”
Philos. Mag.
,
8
(
51
), pp.
569
578
.10.1080/14786441008564913
9.
Ursell
,
F.
,
1947
, “
The Effect of a Fixed Vertical Barrier on Surface Waves in Deep Water
,”
Proc. Camb. Phil. Soc.
,
43
(
3
), pp.
374
382
.10.1017/S0305004100023604
10.
Ursell
,
F.
,
Dean
,
R. G.
, and
Yu
,
Y. S.
,
1960
, “
Forced Small-Amplitude Water Waves: A Comparison of Theory and Experiment
,”
J. Fluid Mech.
,
7
(
1
), pp.
33
52
.10.1017/S0022112060000037
11.
Rhodes-Robinson
,
P. F.
,
1971
, “
On the Forced Surface Waves Due to a Vertical Wave-Maker in the Presence of Surface Tension
,”
Proc. Camb. Phil. Soc.
,
70
(
2
), pp.
323
337
.10.1017/S0305004100049926
12.
Manam
,
S. R.
,
Bhattacharjee
,
J.
, and
Sahoo
,
T.
,
2006
, “
Expansion Formulae in Wave Structure Interaction Problems
,”
Proc. R. Soc. A.
,
462
(2176), pp.
263
287
.10.1098/rspa.2005.1562
13.
Watanabe
,
E.
,
Utsunomiya
,
T.
, and
Wang
,
C. M.
,
2004
, “
Hydroelastic Analysis of Pontoon-Type VLFS: A Literature Survey
,”
Eng. Struct.
,
26
(
2
), pp.
245
256
.10.1016/j.engstruct.2003.10.001
14.
Chen
,
X.
,
Wu
,
Y.
,
Cui
,
W.
, and
Jensen
,
J. J.
,
2006
, “
Review of Hydroelasticity Theories for Global Response of Marine Structures
,”
Ocean Eng.
,
33
(
3–4
), pp.
439
457
.10.1016/j.oceaneng.2004.04.010
15.
Wang
,
C. M.
, and
Tay
,
Z. Y.
,
2011
, “
Very Large Floating Structures: Applications, Research and Development
,”
Procedia Eng.
,
14
, pp.
62
72
.10.1016/j.proeng.2011.07.007
16.
Squire
,
V. A.
,
2007
, “
Of Ocean Waves and Sea-Ice Revisited
,”
Cold Reg. Sci. Technol.
,
49
(
2
), pp.
110
133
.10.1016/j.coldregions.2007.04.007
17.
Squire
,
V. A.
,
2008
, “
Synergies Between VLFS Hydroelasticity and Sea-Ice Research
,”
Int. J. Offshore Polar Eng.
,
18
(
3
), pp.
1
13
.
18.
Korobkin
,
A.
,
Parau
,
E. I.
, and
Vanden-broeck
,
J. M.
,
2011
, “
The Mathematical Challenges and Modeling of Hydroelasticity
,”
Phil. Trans. R. Soc. A
,
373
(2038), pp.
2803
2812
.10.1098/rsta.2011.0116
19.
Schulkes
,
R. M. S. M.
,
Hosking
,
R. J.
, and
Sneyd
,
A. D.
,
1987
, “
Waves Due to a Steadily Moving Source on a Floating Ice Plate. Part 2
,”
J. Fluid Mech.
,
180
, pp.
297
318
.10.1017/S0022112087001812
20.
Bhattacharjee
,
J.
, and
Sahoo
,
T.
,
2008
, “
Flexural Gravity Wave Problems in Two-Layer Fluids
,”
Wave Motion
,
45
(
3
), pp.
133
153
.10.1016/j.wavemoti.2007.04.006
21.
Mondal
,
R.
, and
Sahoo
,
T.
,
2012
, “
Wave Structure Interaction Problems for Two-Layer Fluids in Three Dimensions
,”
Wave Motion
,
49
(
5
), pp.
501
524
.10.1016/j.wavemoti.2012.02.002
22.
Mondal
,
R.
,
Mandal
,
S.
, and
Sahoo
,
T.
,
2014
, “
Surface Gravity Wave Interaction With Circular Flexible Structures
,”
Ocean Eng.
,
88
, pp.
446
462
.10.1016/j.oceaneng.2014.07.008
23.
Mohanty
,
S. K.
,
Mondal
,
R.
, and
Sahoo
,
T.
,
2014
, “
Time Dependent Flexural Gravity Waves in the Presence of Current
,”
J. Fluids Struct.
,
45
, pp.
28
49
.10.1016/j.jfluidstructs.2013.11.018
You do not currently have access to this content.