Wave-ice interactions in the marginal ice zone. Part 1: Theoretical foundations

Ocean Modelling

Volumn 71, Issue , 2013, Pages 81-91

  Williams, Timothy D ^a   Bennetts, Luke G ^b   Squire, Vernon A ^c   Dumont, Dany ^d   Bertino, Laurent ^a,e  

^a NANSEN ENVIRONMENTAL AND REMOTE SENSING CENTER   (Norway)

^b UNIVERSITY OF ADELAIDE   (Australia)

^c UNIVERSITY OF OTAGO   (New Zealand)

^d INSTITUT DES SCIENCES DE LA MER DE RIMOUSKI   (Canada)

^e BJERKNES CENTRE FOR CLIMATE RESEARCH   (Norway)

Author keywords

Ice breakage; Ice ocean modelling; Marginal ice zone; Wave attenuation

Indexed keywords

DISTRIBUTION MODELS; INTERACTION MODEL; MARGINAL ICE ZONE; NUMERICAL WAVE MODELING; OCEAN SURFACE WAVES; PROBABILISTIC APPROACHES; THEORETICAL FOUNDATIONS; WAVE ATTENUATION;

SEA ICE;

WAVE ENERGY CONVERSION;

ICE BREAKUP; MARGINAL ICE ZONE; NUMERICAL MODEL; OCEAN WAVE; SEA ICE; WAVE ATTENUATION; WAVE-ICE INTERACTION;

EID: 84885470354     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2013.05.010     Document Type: Article

References (70)

1. Ardhuin F., Rascle N., Belibassakis K.A. Explicit wave-averaged primitive equations using a generalized Lagrangian mean. Ocean Modell. 2008, 20(1):35-60.
2. Ardhuin F., Rogers E., Babanin A.V., Filipot J.-F., Magne R., Roland A., van der Westhuysen A., Queffeulou P., Lefevre J.-M., Aouf L., Collard F. Semiempirical dissipation source functions for ocean waves. Part I: definition, calibration, and validation. J. Phys. Oceanogr. 2010, 40:1917-1941.
3. Asplin M.G., Galley R., Barber D.G., Prinsenberg S.J. Fracture of summer perennial sea ice by ocean swell as a result of Arctic storms. J. Geophys. Res. 2012, 117. (C06025).
4. Babanin A.V., Ganopolski A., Phillips W.R.C. Wave-induced upper-ocean mixing and climate modelling. Ocean Modell. 2009, 29(3):189-197.
5. Barber D.G., Galley R., Asplin M.G., De Abreu R., Warner K.-A., Pućko M., Gupta M., Prinsenberg S.J., Julien S. Perennial pack ice in the southern Beaufort Sea was not as it appeared in the summer of 2009. Geophys. Res. Lett. 2009, 36. (L24501).
6. Bennetts L., Peter M.A., Squire V.A., Meylan M.H. A three-dimensional model of wave attenuation in the marginal ice zone. J. Geophys. Res. 2010, 115. (C12043).
7. Bennetts L.G., Squire V.A. Model sensitivity analysis of scattering-induced attenuation of ice-coupled waves. Ocean Modell. 2012, 45-46:1-13.
8. Bennetts L.G., Squire V.A. On the calculation of an attenuation coefficient for transects of ice-covered ocean. Proc. R. Soc. London A 2012, 468(2137):136-162.
9. Cartwright D.E., Longuet-Higgins M.S. The statistical distribution of the maxima of a random function. Proc. R. Soc. London A 1956, 237(1209):212-232.
10. Cole D.M. Modeling the cyclic loading response of sea ice. Int. J. Solids Struct. 1998, 35(31-32):4067-4075.
11. De Carolis G., Desiderio D. Dispersion and attenuation of gravity waves in ice: a two-layer viscous fluid model with experimental data validation. Phys. Lett. A 2002, 305:399-412.
12. Doble, M.J., Bidlot, J.-R., 2013. Wavebuoy measurements at the Antarctic sea ice edge compared with an enhanced ECMWF WAM: progress towards global waves-in-ice modeling. Ocean Modell. (in press), http://dx.doi.org/10.1016/j.ocemod.2013.05.012.
13. Dumont D., Kohout A.L., Bertino L. A wave-based model for the marginal ice zone including a floe breaking parameterization. J. Geophys. Res. 2011, 116(C4):1-12.
14. Feltham D.L. Granular flow in the marginal ice zone. Philos. Trans. R. Soc. London A 2005, 363:1677-1700.
15. Fox C., Squire V.A. Strain in shore fast ice due to incoming ocean waves and swell. J. Geophys. Res. 1991, 96(C3):4531-4547.
16. Frankenstein G.E., Gardner S. Equations for determining the brine volume of sea ice from -0.5 to 22.9°C. J. Glaciol. 1967, 6:943-944.
17. Gelci R., Cazalé H., Vassal J. Prévision de la houle. La méthode des densités spectroangulaires. Bull. Inf. Comité Central Oceanogr. d'Etude CÔtes 1957, 9:416-435.
18. Girard L., Amitrano D., Weiss J. Failure as a critical phenomenon in a progressive damage model. J. Stat. Mech.: Theory Exp. 2010, P01013.
19. Girard L., Weiss J., Molines J.M., Barnier B., Bouillon S. Evaluation of high-resolution sea ice models on the basis of statistical and scaling properties of Arctic sea ice drift and deformation. J. Geophys. Res. 2009, 114. (C08015).
20. Hasselmann K. Grundgleichungen der seegangsvoraussage. Schiffstechnik 1960, 7:191-195.
21. Hasselmann K. On the non-linear transfer in a gravity-wave spectrum. Part 1. General Theory. J. Fluid Mech. 1962, 12:481-500.
22. Hasselmann K. On the non-linear transfer in a gravity-wave spectrum. Part 3. Computation of the energy flux and swell-sea interaction for a Neumann spectrum. J. Fluid Mech. 1963, 15:385-398.
23. Herman A. Sea-ice floe-size distribution in the context of spontaneous scaling emergence in stochastic systems. Phys. Rev. E 2010, 81:066123.
24. Herman A. Molecular-dynamics simulation of clustering processes in sea-ice floes. Phys. Rev. E 2011, 84:056104.
25. Herman A. Numerical modeling of force and contact networks in fragmented sea ice. Ann. Glaciol. 2013, 54(62):114-120.
26. Hibler W.D. A dynamic thermodynamic sea ice model. J. Phys. Oceanogr. 1979, 9:815-846.
27. Holt B., Martin S. The effect of a storm on the 1992 summer sea ice cover of the Beaufort, Chukchi, and East Siberian Seas. J. Geophys. Res. 2001, 106(C1):1017-1032.
28. Howells The multiple scattering of waves by weak random irregularities in the medium. Proc. R. Soc. A 1960, 252:431-462.
29. Hunke E.C., Dukowicz J.K. An elastic-viscous-plastic model for sea ice dynamics. J. Phys. Oceanogr. 1997, 27:1849-1867.
30. Keller J.B. Gravity waves on ice-covered water. J. Geophys. Res. 1998, 103(C4):7663-7670.
31. Kohout A., Meylan M., Plew D.R. Wave attenuation in a marginal ice zone due to the bottom roughness of ice floes. Ann. Glaciol. 2011, 52(57):118-122.
32. Kohout A.L., Meylan M.H. An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone. J. Geophys. Res. 2008, 113. (C09016). 10.1029/2007JC004434.
33. Langhorne P.J., Squire V.A., Fox C., Haskell T.G. Break-up of sea ice by ocean waves. Ann. Glaciol. 1998, 27:438-442.
34. Langhorne P.J., Squire V.A., Fox C., Haskell T.G. Lifetime estimation for a land-fast ice sheet subjected to ocean swell. Ann. Glaciol. 2001, 33:333-338.
35. Langleben M.P., Pounder E.R. Elastic parameters of sea ice. Ice and Snow 1963, 69-78. MIT Press, USA. W.D. Kingery (Ed.).
36. Longuet-Higgins M.S. On the statistical distribution of the heights of sea waves. J. Mar. Res. 1952, 11:245-266.
37. Longuet-Higgins M.S. On the distribution of the heights of sea waves: Some effects of nonlinearity and finite band width. J. Geophys. Res. 1980, 85(C3):1519-1523.
38. Marchenko, A.V., Shestov, A., Karulin, E., Morozov, E., Karulina, M., Bogorodsky, P., Muzylev, S.V., Onishchenko, D., Makshtas, A., 2011. Field studies of sea water and ice properties in Svalbard fjords. In: Proceedings of the 21st International Conference on Port and Ocean Engineering under Arctic Conditions, Montréal, Canada, pp. 148-160.
39. Masson D., LeBlond P.H. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 1989, 202:111-136.
40. Matsushita M. Fractal viewpoint of fracture and accretion. J. Phys. Soc. Jpn. 1985, 54(3):857-860.
41. Mellor, M., 1986. The mechanics of sea ice. In: Untersteiner, N. (Ed.), The Geophysics of Sea Ice. pp. 165-182.
42. Meylan M., Squire V., Fox C. Toward realism in modelling ocean wave behaviour in marginal ice zones. J. Geophys. Res.-Oceans 1997, 102(C10):22981-22991.
43. Meylan M.H., Masson D. A linear Boltzmann equation to model wave scattering in the marginal ice zone. Ocean Modell. 2006, 11(3-4):417-427.
44. Perrie W., Hu Y. Air-ice-ocean momentum exchange. Part 1: Energy transfer between waves and ice floes. J. Phys. Oceanogr. 1996, 26:1705-1720.
45. Polnikov V., Lavrenov I. Calculation of the nonlinear energy transfer through the wave spectrum at the sea surface covered with broken ice. Oceanology 2007, 47:334-343.
46. Prinsenberg S.J., Peterson I.K. Observing regional-scale pack-ice decay processes with helicopter-borne sensors and moored upward-looking sonars. Ann. Glaciol. 2011, 52(57):35-42.
47. Rampal P., Weiss J., Marsan D., Lindsay R., Stern H. Scaling properties of sea ice deformation from buoy dispersion analysis. J. Geophys. Res. 2008, 113. (C03002).
48. Robinson N.J., Palmer S.C. A modal analysis of a rectangular plate floating on an incompressible fluid. J. Sound Vib. 1990, 142:453-460.
49. Rothrock D.A., Thorndike A.S. Measuring the sea ice floe size distribution. J. Geophys. Res. 1984, 89(C4):6477-6486.
50. Shen H.H., Hibler W.D., Leppäranta M. On applying granular flow theory to a deforming broken ice field. Acta Mech. 1986, 63:143-160.
51. Shen H.H., Sankaran B. Internal length and time scales in a simple shear granular flow. Phys. Rev. E 2004, 70. (051308).
52. Squire V., Moore S.C. Direct measurement of the attenuation of ocean waves by pack ice. Nature 1980, 283(5745):365-368.
53. Steele M. Sea ice melting and floe geometry in a simple ice-ocean model. J. Geophys. Res. 1992, 97(C11):17,729-17,738.
54. Steele M., Morison J.H., Untersteiner N. The partition of air-ice-ocean momentum exchange as a function of ice concentration, floe size, and draft. J. Geophys. Res. 1989, 94(C9):12,739-12,750.
55. Stephenson S.R., Smith L.C., Agnew J.A. Divergent long-term trajectories of human access to the Arctic. Nat. Clim. Change 2011, 1:156-160.
56. Timco G.W., O'Brien S. Flexural strength equation for sea ice. Cold Regions Sci. Tech. 1994, 22:285-298.
57. Timco G.W., Weeks W.F. A review of the engineering properties of sea ice. Cold Regions Sci. Tech. 2010, 60:107-129.
58. Toyota, T., Enomoto, H., 2002. Analysis of sea ice floes in the Sea of Okhotsk using ADEOS/AVNIR images. In: Proc. 16th Int. Symposium on Ice, International Association for Hydro-Environment Engineering and Research, Dunedin, New Zealand, pp. 211-217.
59. Toyota T., Haas C., Tamura T. Size distribution and shape properties of relatively small sea-ice floes in the Antarctic marginal ice zone in late winter. Deep-Sea Res. II 2011, 58(9-10):1182-1193.
60. Toyota T., Takatsuji S., Nakayama M. Characteristics of sea ice floe size distribution in the seasonal ice zone. Geophys. Res. Lett. 2006, 33. (L02616).
61. Vaughan G.L., Squire V.A. Wave induced fracture probabilities for Arctic sea-ice. Cold Regions Sci. Tech. 2011, 67(1-2):31-36.
62. Wadhams P., Squire V.A., Goodman D.J., Cowan A.M., Moore S.C. The attenuation rates of ocean waves in the marginal ice zone. J. Geophys. Res. 1988, 93(C6):6799-6818.
63. WAMDI Group, 1988. The WAM model-A third generation ocean wave prediction model. J. Phys. Oceanogr. 18, 1775-1810.
64. Wang R., Shen H.H. A continuum model for the linear wave propagation in ice-covered oceans: an approximate solution. Ocean Modell. 2011, 38:244-250.
65. Wang R., Shen H.H. Gravity waves propagating into an ice-covered ocean: a viscoelastic model. J. Geophys. Res. 2011, 115. (C06024). 10.1029/2009JC005591.
66. Weber J.E. Wave attenuation and wave drift in the marginal ice zone. J. Phys. Oceanogr. 1987, 17:2351-2361.
67. Weeks W.F., Tucker W.B., Frank M., Fungcharoen S. Characteristics of surface roughness and floe geometry of sea ice over the continental shelves of the Beaufort and Chukchi Seas. Sea Ice Processes and Models 1980, 300-312. University of Washington Press, Seatle. R.S. Pritchard (Ed.).
68. Williams, T.D., Bennetts, L.G., Squire, V.A., Dumont, D., Bertino, L., 2013. Wave-ice interactions in the marginal ice zone. Part 2: numerical implementation and sensitivity studies along 1D transects of the ocean surface. Ocean Modell. (submitted for publication), http://dx.doi.org/10.1016/j.ocemod.2013.05.011.
69. Williams T.D., Porter R. The effect of submergence on the scattering by the interface between two semi-infinite sheets. J. Fluids Struct. 2009, 25:777-793.
70. World Meteorological Organization, 1998. Guide to Wave Forecasting and Analysis, 2nd ed. WMO No. 702. World Meteorological Organization.