Wave propagation across sea-ice thickness changes

Ocean Modelling

Volumn 21, Issue 1-2, 2008, Pages 1-11

  Squire, V A ^a   Williams, T D ^b  

^a UNIVERSITY OF OTAGO   (New Zealand)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Finite draft; Geophysical comparison with zero draft results; Green's function method; Sea ice; Wave ice interaction

Indexed keywords

BOUNDARY CONDITIONS; GREEN'S FUNCTION; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; SEA ICE; SURFACE WAVES; TRANSITION FLOW; WATER WAVES; WAVE PROPAGATION;

FINITE DRAFT; PROBABILITY DENSITY DISTRIBUTION; WAVE-ICE INTERACTION;

OCEANOGRAPHY;

CLIMATE CHANGE; GREEN FUNCTION; ICE COVER; ICE SHEET; ICE THICKNESS; SEA ICE; SUBMERGENCE; WAVE ENERGY; WAVE PROPAGATION; WAVE SCATTERING; WAVE-ICE INTERACTION; WAVELENGTH;

EID: 38749130460     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2007.10.006     Document Type: Article

References (65)

1. Andrianov A.I., and Hermans A.J. Hydroelastic analysis of floating plate of finite draft. In: Grue J. (Ed). Proceedings 20th International Workshop on Water Waves and Floating Bodies (2005), University of Oslo, Oslo, Norway.
2. Balmforth N.J., and Craster R.V. Ocean waves and ice sheets. J. Fluid Mech. 395 (1999) 89-124
3. Barrett M., and Squire V.A. Ice-coupled wave propagation across an abrupt change in ice rigidity, density or thickness. J. Geophys. Res. 101 C9 (1996) 20825-20832
4. Bennetts L.G., Biggs N.R.T., and Porter D. A multi-mode approximation to wave scattering by ice sheets of varying thickness. J. Fluid Mech. 579 (2007) 413-443
5. Berry M.V., and Klein S. Transparent mirrors: rays, waves and localization. Eur. J. Phys. 18 3 (1997) 222-228
6. Bishop R.E.D., and Price W.G. Hydroelasticity of Ships (1979), Cambridge University Press, Cambridge
7. Bishop R.E.D., Price W.G., and Wu Y. A general linear hydroelasticity theory of floating structures moving in a seaway. Philos. T. Roy. Soc. A 316 1538 (1986) 375-426
8. Chakrabarti A. On the solution of the problem of scattering of surface-water waves by the edge of an ice cover. Proc. R. Soc. Lon. Ser-A 456 1997 (2000) 1087-1099
9. Chou T. Band structure of surface flexural-gravity waves along periodic interfaces. J. Fluid Mech. 369 (1998) 333-350
10. Chung H., and Fox C. Propagation of flexural-gravity waves at the interface between floating plates. Int. J. Offshore Polar 12 3 (2002) 163-170
11. Chung H., and Linton C.M. Reflection and transmission of waves across a gap between two semi-infinite elastic plates on water. Q.J. Mech. Appl. Math. 58 1 (2005) 1-15
12. Comiso J. A rapidly declining perennial sea-ice cover in the Arctic. Geophys. Res. Lett. 29 20 (2002) 1956 10.1029/2002GL015650
13. Eatock Taylor R. Wet or dry modes in linear hydroelasticity - why modes?. In: Eatock Taylor R. (Ed). Proceedings of 3rd International Conference on Hydroelasticity in Marine Technology (2003), University of Oxford, Oxford, UK 239-250
14. Eatock Taylor R. Hydroelastic analysis of plates and some approximations. J. Eng. Math. 58 1-4 (2007) 267-278
15. Evans, D.V., Davies, T.V., 1968. Wave-ice interaction. Tech. Rep. 1313, Davidson Laboratory, Stevens Institute of Technology, New Jersey.
16. Evans D.V., and Porter R. Wave scattering by narrow cracks in ice sheets floating on water of finite depth. J. Fluid Mech. 484 (2003) 143-165
17. Fox C., and Squire V.A. Reflection and transmission characteristics at the edge of shore fast sea ice. J. Geophys. Res. 95 (1990) 11629-11639
18. Fox C., and Squire V.A. Coupling between an ocean and an ice shelf. Ann. Glaciol. 15 (1991) 101-108
19. Fox C., and Squire V.A. On the oblique reflexion and transmission of ocean waves from shore fast sea ice. Philos. T. Roy. Soc. A 347 1682 (1994) 185-218
20. Hermans A.J. Free-surface wave interaction with a thick flexible dock or very large floating platform. J. Eng. Math. 58 1-4 (2007) 77-90
21. Hunkins K. Waves on the Arctic Ocean. J. Geophys. Res. 67 6 (1962) 2477-2489
22. Kohout A.L., and Meylan M.H. A model for wave scattering in the marginal ice zone based on a two-dimensional floating elastic plate solution. Ann. Glaciol. 44 (2006) 101-107
23. Kreisel G. Surface waves. Q. Appl. Math. 7 (1949) 21-44
24. Langhorne P.J., Squire V.A., and Haskell T.G. Breakup of sea ice by ocean waves. Ann. Glaciol. 27 (1998) 438-442
25. Langhorne P.J., Squire V.A., and Haskell T.G. Lifetime estimation for a fast ice sheet subjected to ocean swell. Ann. Glaciol. 33 (2001) 333-338
26. Linton C., and McIver P. Handbook of Mathematical Techniques for Wave/Structure Interactions (2001), CRC Press, Boca Raton, FL
27. Linton C.M., and Chung H. Reflection and transmission at the ocean/sea-ice boundary. Wave Motion 38 1 (2003) 43-52
28. Manam S.R., Bhattacharjee J., and Sahoo T. Expansion formulae in wave structure interaction problems. Proc. R. Soc. Lon. Ser-A 462 2065 (2006) 263-287
29. Marchenko A.V. Flexural gravity wave diffraction at linear irregularities in sheet ice. Fluid Dyn. 32 4 (1997) 548-560
30. Meylan, M.H., 1993. The behaviour of sea ice in ocean waves. Ph.D. thesis, University of Otago, Dunedin, New Zealand.
31. Meylan M.H., and Squire V.A. The response of ice floes to ocean waves. J. Geophys. Res. 99 C1 (1994) 899-900
32. Meylan M.H., and Squire V.A. Response of a circular ice floe to ocean waves. J. Geophys. Res. 101 C4 (1996) 8869-8884
33. Meylan M.H., Squire V.A., and Fox C. Toward realism in modelling ocean wave behaviour in marginal ice zones. J. Geophys. Res. 102 C10 (1997) 22981-22991
34. Mindlin R.D. Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. 18 (1951) 31-38
35. Nagurny A.P., Korostolev V.G., and Abaza V.P. A method for determination of effective sea ice thickness in the Arctic basin for climate monitoring. Bull. Russ. Acad. Sci. Phys. Suppl. Phys. Vib. 58 (1994) 168-174
36. Newman J.N. Marine Hydrodynamics (1977), MIT Press, Cambridge, MA
37. Newman J.N. Wave effects on deformable bodies. Appl. Ocean Res. 16 1 (1994) 47-59
38. Pedersen, L.T., 14th September 2007. European Space Agency Portal. .
39. Peter M.A., Meylan M.H., and Linton C.M. Water-wave scattering by a periodic array of arbitrary bodies. J. Fluid Mech. 548 (2006) 237-256
40. Pierson W.J., and Moskowitz L. A proposed spectral form for fully developed wind seas based on the similarity theory of S.A. Kitaigorodskii. J. Geophys. Res. 69 (1964) 5181-5190
41. Porter D., and Porter R. Approximations to wave scattering by an ice sheet of variable thickness over undulating bed topography. J. Fluid Mech. 509 (2004) 145-179
42. Rothrock D.A., Yu Y., and Maykut G.A. Thinning of the Arctic sea-ice cover. Geophys. Res. Lett. 26 23 (1999) 3469-3472
43. Sahoo T., Yip T.L., and Chwang A.T. Scattering of surface waves by a semi-infinite floating elastic plate. Phys. Fluids 13 11 (2001) 3215-3222
44. Sarpkaya T., and Isaacson M. Mechanics of Wave Forces on Offshore Structures (1981), Van Nostrand Reinhold, New York
45. Squire V.A. Of ocean waves and sea-ice revisited. Cold Reg. Sci. Technol. 49 2 (2007) 110-133
46. Squire V.A., and Dixon T.W. An analytic model for wave propagation across a crack in an ice sheet. Int. J. Offshore Polar 10 3 (2000) 173-176
47. Squire V.A., and Dixon T.W. How a region of cracked sea ice affects ice-coupled wave propagation. Ann. Glaciol. 33 (2001) 327-332
48. Squire V.A., and Dixon T.W. On modelling an iceberg embedded in shore fast sea ice. J. Eng. Math. 40 3 (2001) 211-236
49. Squire V.A., Dugan J.P., Wadhams P., Rottier P.J., and Liu A.K. Of ocean waves and sea ice. Annu. Rev. Fluid Mech. 27 (1995) 115-168
50. Tkacheva L.A. Scattering of surface waves by the edge of a floating elastic plate. J. Appl. Mech. Tech. Phys. 42 4 (2001) 638-646
51. Tkacheva L.A. Diffraction of surface waves at floating elastic plate. In: Rainey R.C.T., and Lee S.F. (Eds). Proceedings of the 17th International Workshop on Water Waves and Floating Bodies (2002), The Royal Institution of Naval Architects, Cambridge, England.
52. Tkacheva L.A. The diffraction of surface waves by a floating elastic plate at oblique incidence. J. Appl. Math. Mech. 68 3 (2004) 425-436
53. Vaughan G.L., and Squire V.A. Scattering of ice-coupled waves by variable sea-ice terrain. Ann. Glaciol. 44 (2006) 88-94
54. Vaughan G.L., and Squire V.A. Scattering of ice-coupled waves by a sea-ice sheet with random thickness. Wave Random Complex 17 3 (2007) 357-380
55. Vaughan G.L., Williams T.D., and Squire V.A. Perfect transmission and asymptotic solutions for reflection of ice-coupled waves by inhomogeneities. Wave Motion 44 5 (2007) 371-384
56. Wadhams P. Sea ice morphology. In: Lepparanta M. (Ed). Physics of Ice Covered Seas vol. 1 (1988), Helsinki University Printing House, Finland 231-287
57. Wadhams P., and Davis N.R. Further evidence of ice thinning in the Arctic Ocean. Geophys. Res. Lett. 27 24 (2000) 3973-3976
58. Williams, T.D., 2005. Reflections on ice: the scattering of flexural-gravity waves by irregularities in Arctic and Antarctic ice sheets. Ph.D. thesis, University of Otago, Dunedin, New Zealand.
59. Williams T.D., and Squire V.A. Wave propagation across an oblique crack in an ice sheet. Int. J. Offshore Polar 12 3 (2002) 157-162
60. Williams T.D., and Squire V.A. Oblique scattering of plane flexural-gravity waves by heterogeneities in sea ice. Proc. R. Soc. Lon. Ser-A 460 2052 (2004) 3469-3497
61. Williams T.D., and Squire V.A. The scattering of flexural-gravity waves by an ice field. Int. J. Offshore Polar 14 3 (2004) 161-168
62. Williams T.D., and Squire V.A. Scattering of flexural-gravity waves at the boundaries between three floating sheets with applications. J. Fluid Mech. 569 (2006) 113-140
63. Williams T.D., and Squire V.A. Wave scattering at the sea-ice/ice-shelf transition with other applications. SIAM J. Appl. Math. 67 4 (2007) 938-959
64. Williams, T.D., Squire, V.A., in press. The effect of submergence on wave scattering across a transition between two floating flexible plates. Wave Motion.
65. Wu C., Watanabe E., and Utsunomiya T. An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate. Appl. Ocean Res. 17 5 (1995) 301-310