Modeling ocean wave propagation under sea ice covers

Acta Mechanica Sinica/Lixue Xuebao

Volumn 31, Issue 1, 2015, Pages

  Zhao, Xin ^a   Shen, Hayley H ^a   Cheng, Sukun ^a  

^a Clarkson University   (United States)

Author keywords

Cryospheric change; Ocean waves; Sea ice

Indexed keywords

AGGREGATES; GLACIERS; OCEANOGRAPHY; SEA ICE; VISCOELASTICITY; WAVE ENERGY CONVERSION; WAVE PROPAGATION;

CRYOSPHERIC CHANGE; FUNDAMENTAL RESEARCH; LABORATORY EXPERIMENTS; RESEARCH METHODOLOGIES; THEORETICAL FRAMEWORK; THIN ELASTIC PLATES; VISCOELASTIC MODELING; WAVE REFLECTION AND TRANSMISSIONS;

WATER WAVES;

EID: 84924139498     PISSN: 05677718     EISSN: 16143116     Source Type: Journal    
DOI: 10.1007/s10409-015-0017-5     Document Type: Review

References (92)

1. Komen, G.J., Cavaleri, L., Donelan, M., et al.: Dynamics and Modeling of Ocean Waves. Cambridge University Press, USA (1996)
2. Thomson, J., Rogers, W.E.: Swell and sea in the emerging Arctic Ocean. Geophysical Research Letters 41, 3136–3140 (2014)
3. Wadhams, P.: Ice In the Ocean. CRC Press, Amsterdam (2000)
4. Toyota, T., Takatsuji, S., Nakayama, M.: Characteristics of sea ice floe size distribution in the seasonal ice zone. Geophysical Research Letters 33, L02616 (2006)
5. Perrie, W., Hu, Y.: Air-ice-ocean momentum exchange. Part II: Ice drift. J. Phys. Oceanogr. 27, 1976–1996 (1997)
6. Dai, M., Shen, H.H., Hopkins, M.A., et al.: Wave rafting and the equilibrium pancake ice cover thickness. Journal of Geophysical Research: Oceans (1978–2012) 109, C07023 (2004)
7. Tolman, H.L.: Treatment of unresolved islands and ice in wind wave models. Ocean Modelling 5, 219–231 (2003)
8. Kohout, A.L., Williams, M.J.M., Dean, S.M., et al.: Storminduced sea-ice breakup and the implications for ice extent. Nature 509, 604–607 (2014)
9. Wadhams, P., Squire, V.A., Goodman, D.J., et al.: The attenuation rates of ocean waves in the marginal ice zone. Journal of Geophysical Research: Oceans (1978–2012) 93, 6799–6818 (1988)
10. Squire, V.A., Dugan, J.P., Wadhams, P., et al.: Of ocean waves and sea ice. Annual Review of Fluid Mechanics 27, 115–168 (1995)
11. Squire, V.A.: Of ocean waves and sea-ice revisited. Cold Regions Science and Technology 49, 110–133 (2007)
12. Dumont, D., Kohout, A., Bertino, L.: A wave-based model for the marginal ice zone including a floe breaking parameterization. Journal of Geophysical Research: Oceans (1978–2012) 116, C04001 (2011)
13. Masson, D., LeBlond, P.H.: Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. Journal of Fluid Mechanics 202, 43–81 (1989)
14. Perrie, W., Hu, Y.: Air-ice-ocean momentum exchange. Part 1: Energy transfer between waves and ice floes. Journal of Physical Oceanography 26, 1705–1720 (1996)
15. 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 Research Part II: Topical Studies in Oceanography 58, 1182–1193 (2011)
16. Peters, A.S.: The effect of a floating mat on water waves. Communications on Pure and Applied Mathematics 3, 319–354 (1950)
17. Weitz, M., Keller, J.B.: Reflection of water waves from floating ice in water of finite depth. Communications on Pure and Applied Mathematics 3, 305–318 (1950)
18. Wadhams, P.: The seasonal ice zone//The Geophysics of Sea Ice. 825-991, Springer. US (1986)
19. Fox, C., Squire, V.A.: Reflection and transmission characteristics at the edge of shore fast sea ice. Journal of Geophysical Research: Oceans (1978–2012) 95, 11629–11639 (1990)
20. Fox, C., Squire, V.A.: On the oblique reflexion and transmission of ocean waves at shore fast sea ice. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences 347, 185–218 (1994)
21. Barrett, M.D., Squire, V.A.: Ice-coupled wave propagation across an abrupt change in ice rigidity, density, or thickness. Journal of Geophysical Research: Oceans (1978–2012) 101, 20825–20832 (1996)
22. Keller, J.B.: Gravity waves on ice-covered water. Journal of Geophysical Research: Oceans (1978–2012) 103, 7663–7669 (1998)
23. De Carolis, G., Desiderio, D.: Dispersion and attenuation of gravity waves in ice: A two-layer viscous fluid model with experimental data validation. Physics Letters A 305, 399–412 (2002)
24. Wang, R., Shen, H.H.: Gravity waves propagating into an icecovered ocean: A viscoelastic model. Journal of Geophysical Research: Oceans (1978–2012) 115, 399–412 (2010)
25. Tolman, H.L.: User manual and system documentation of WAVEWATCH III TM version 4.18b, 307 (2014)
26. Miles, J.W.: On the generation of surface waves by shear flows. Journal of Fluid Mechanics 3, 185–204 (1957)
27. Gent, P.R., Taylor, P.A.: A numerical model of the air flow above water waves. Journal of Fluid Mechanics 77, 105–128 (1976)
28. Riley, D.S., Donelan, M.A., Hui, W.H.: An extended Miles’ theory for wave generation by wind. Boundary-Layer Meteorology 22, 209–225 (1982)
29. Al-Zanaidi, M.A., Hui, W.H.: Turbulent airflow over water waves-a numerical study. Journal of Fluid Mechanics 148, 225–246 (1984)
30. Jacobs, S.J.: An asymptotic theory for the turbulent flow over a progressive water wave. Journal of Fluid Mechanics 174, 69–80 (1987)
31. Chalikov, D.V., Makin, V.K.: Models of the wave boundary layer. Boundary-Layer Meteorology 56, 83–99 (1991)
32. Hasselmann, K.: On the non-linear energy transfer in a gravitywave spectrum Part 1: General theory. Journal of Fluid Mechanics 12, 481–500 (1962)
33. Hasselmann, K.: On the non-linear energy transfer in a gravity wave spectrum. Part 2: Conservation theorems; wave-particle analogy; irrevesibility. Journal of Fluid Mechanics 15, 273–281 (1963)
34. Hasselmann, K.: On the non-linear energy transfer in a gravitywave spectrum. Part 3: Evaluation of the energy flux and swell-sea interaction for a Neumann spectrum. Journal of Fluid Mechanics 15, 385–398 (1963)
35. Zakharov, V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. Journal of Applied Mechanics and Technical Physics 9, 190–194 (1968)
36. Janssen, P.: The Interaction of Ocean Waves and Wind. Cambridge University Press, USA (2004)
37. Hasselmann, K.: On the spectral dissipation of ocean waves due to white capping. Boundary-Layer Meteorology 6, 107–127 (1974)
38. Phillips, O.M.: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. Journal of Fluid Mechanics 156, 505–531 (1985)
39. Jenkins, A.D.: A Lagrangian model for wind- and wave-induced near-surface currents. Coastal Engineering 11, 513–526 (1987)
40. Rogers, W.E., Orzech, M.D.: Implementation and testing of ice and mud source functions in WAVEWATCH III. NRL Memorandum Report. NRL/MR/7320-13-9462, 31 (2013)
41. Gaster, M.: A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. Journal of Fluid Mechanics 14, 222–224 (1962)
42. Liu, A.K., Mollo-Christensen, E.: Wave propagation in a solid ice pack. Journal of Physical Oceanography 18, 1702–1712 (1988)
43. Meylan, M.H., Squire, V.A., Fox, C.: Toward realism in modeling ocean wave behavior in marginal ice zones. Journal of Geophysical Research: Oceans (1978–2012) 102, 22981–22991 (1997)
44. Meylan, M.H., Masson, D.: A linear Boltzmann equation to model wave scattering in the marginal ice zone. Ocean Modelling 11, 417–427 (2006)
45. Liu, A.K., Holt, B., Vachon, P.W.: Wave propagation in the marginal ice zone: Model predictions and comparisons with buoy and synthetic aperture radar data. Journal of Geophysical Research: Oceans (1978–2012) 96, 4605–4621 (1991)
46. Squire, V.A., Allan, A.J.: Propagation of flexural gravity waves in sea ice, in Sea Ice Processe and Models. In: Proceedings of the Arctic Ice Dynamics Joint Experiment, Pritchard, R. S. edn. 327–338, University of Washington Press, Seattle (1980)
47. Shen, H.H., Squire, V.A.: Wave damping in compact pancake ice fields due to interactions between pancakes. Antarctic Sea Ice: Physical Processes, Interactions and Variability 74, 325–341 (1998)
48. Wang, R.X.: Water Wave Propagation in Ice-Covered Oceans, [Ph.D. Thesis]. Clarkson University, USA (2010)
49. Lange, M.A., Ackley, S.F., Wadhams, P., et al.: Development of sea ice in the Weddell Sea. Ann. Glaciol. 12, 92–96 (1989)
50. Squire, V.A.: A comparison of the mass-loading and elastic plate models of an ice field. Cold Regions Science and Technology 21, 219–229 (1993)
51. Sakai, S., Hanai, K.: Empirical formula of dispersion relation of waves in sea ice. In: Ice in the Environment. Proceedings of the 16th IAHR International Symposium on Ice 327–335 (2002)
52. Newyear, K., Martin, S.: A comparison of theory and laboratory measurements of wave propagation and attenuation in grease ice. Journal of Geophysical Research: Oceans (1978–2012) 102, 25091–25099 (1997)
53. Newyear, K., Martin, S.: Comparison of laboratory data with a viscous two layer model of wave propagation in grease ice. Journal of Geophysical Research: Oceans (1978–2012) 104, 7837–7840 (1999)
54. Bennetts, L.G., Squire, V.A.: On the calculation of an attenuation coefficient for transects of ice-covered ocean. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 468, 136–162 (2012)
55. Bennetts, L.G., Squire, V.A.: Model sensitivity analysis of scattering-induced attenuation of ice-coupled waves. Ocean Modelling 45, 1–13 (2012)
56. Meylan M., Squire, V.A.: The response of ice floes to ocean waves. Journal of Geophysical Research: Oceans (1978–2012) 99, 891–900 (1994)
57. Kohout, A.L.: Water wave scattering by floating elastic plates with application to sea ice, [Ph.D Thesis]. University of Auckland, USA (2008)
58. Kohout, A.L., Meylan, M.H., Sakai, S., et al.: Linear water wave propagation through multiple floating elastic plates of variable properties. Journal of fluids and structures, 23, 649–663 (2007)
59. Wang, R., Shen, H.H.: A continuum model for the linear wave propagation in ice-covered oceans: An approximate solution. Ocean Modelling 38, 244–250 (2011)
60. Zhao, X., Shen, H.H.: Ocean wave transmission and reflection between two connecting viscoelastic ice covers: An approximate solution. Ocean Modelling 71, 102–113 (2013)
61. Sarpkaya, T., Isaacson, M.: Mechanics of Wave Forces on Off-shore Structures. Van Nostrand Reinhold Company, New York (1981)
62. Meylan, M.H., Squire, V.A.: Response of a circular ice floe to ocean waves. Journal of Geophysical Research: Oceans (1978–2012) 101, 8869–8884 (1996)
63. Zhao, X., Shen, H.H.; Ocean wave transmission and reflection between two connecting viscoelastic ice covers: A variational approach, to be submitted (2014)
64. Meylan, M.H.: Wave response of an ice floe of arbitrary geometry. Journal of Geophysical Research: Oceans (1978–2012) 107, 5-1–5-11 (2002)
65. Kohout, A.L., Meylan, M.H.: An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone. Journal of Geophysical Research: Oceans (1978–2012) 113, C09016 (2008)
66. Dumont, D., Kohout, A., Bertino, L.: A wave-based model for the marginal ice zone including a floe breaking parameterization. Journal of Geophysical Research: Oceans (1978–2012) 116, C04001 (2011)
67. Williams, T.D., Bennetts, L.G., Squire, V.A., et al.: Waveice interactions in the marginal ice zone. Part 1: Theoretical foundations. Ocean Modelling 71, 81–91 (2013)
68. Williams, T.D., Bennetts, L.G., Squire, V.A., et al.: Waveice interactions in the marginal ice zone. Part 2: Numerical implementation and sensitivity studies along 1D transects of the ocean surface. Ocean Modelling 71, 92–101 (2013)
69. Harms, V.W.: Steady wave-drift of modeled ice floes. Journal of Waterway, Port, Coastal, and Ocean Engineering 113, 606–622 (1987)
70. Huang, G., Law, A.W.K., Huang Z.: Wave-induced drift of small floating objects in regular waves. Ocean Engineering 38, 712–718 (2011)
71. Huang, G., Law, A.W.K.: Wave-induced drift of large floating objects in regular waves. Journal of Waterway, Port, Coastal, and Ocean Engineering 139, 535–542 (2013)
72. Montiel, F., Bonnefoy, F., Ferrant, P., et al.: Hydroelastic response of floating elastic discs to regular waves. Part 1: Wave basin experiments. Journal of Fluid Mechanics 723, 604–628 (2013)
73. Montiel, F., Bennetts, L.G., Squire, V.A., et al.: Hydroelastic response of floating elastic discs to regular waves. Part 2: Modal analysis. Journal of Fluid Mechanics 723, 629–652 (2013)
74. Toyota, T.: A study on growth processes of sea ice in the southern region of the Okhotsk sea, evaluated from heat budget and sea ice sample analysis, [Ph.D. Thesis]. Hokkaido University, Japan (1998)
75. Shen, H.H., Ackley, S.F., Yuan, Y.: Limiting diameter of pancake ice. Journal of Geophysical Research: Oceans (1978–2012) 109, C12035 (2004)
76. Wang, R., Shen, H.H., Evers, K.U.: An experimental study of wave induced ice production. In: Proceedings of the 19th IAHR International Symposium on Ice, Vancouver, Canada, July 6–11 (2008)
77. Callinan, C., Evers, K.U., Wilkinson, J., et al.: Wave propagation in frazil/pancake and fragmented ice covers Part I: Description of the laboratory study. In: Proceedings of the 22nd IAHR Ice Symposium, Aug. 11–15, Singapore (2014)
78. Zhao, X., Callinan, C., Shen, H.H.: Wave propagation in frazil/pancake and fragmented ice covers Part II: Preliminary data analysis. Proceedings of the 22nd IAHR Ice Symposium, Aug. 11–15, Singapore (2014)
79. Lansing, A.: Endurance: Shackletons Incredible Voyage, (2nd ed.) Carroll and Graf Publishers. ISBN 0-7867-0621-X, 288p (1959)
80. Squire, V.A., Moore, S.C.: Direct measurement of the attenuation of ocean waves by pack ice. Nature 283, 365–368 (1980)
81. Wadhams, P., Squire, V.A., Ewing, J.A., et al.: The effect of the marginal ice zone on the directional wave spectrum of the ocean. Journal of Physical Oceanography 16, 358–376 (1986)
82. Frankenstein, S., Loset, S., Shen, H.H.: Wave-ice interactions in Barents Sea marginal ice zone. Journal of Cold Regions Engineering 15, 91–102 (2001)
83. McKenna, R.F., Crocker, G.B.: Ice floe collisions interpreted from acceleration data during LIMEX 89. Atmosphere-Ocean 30, 246–269 (1992)
84. Rottier, P.J.: Floe pair interaction event rates in the marginal ice zone. Journal of Geophysical Research: Oceans (1978–2012) 97, 9391–9400 (1992)
85. Campbell, A.J., Bechle, A.J., Wu, C.H.: Observations of surface waves interacting with ice using stereo imaging. Journal of Geophysical Research: Oceans 119, 266–284 (2014)
86. Ailliot, P., Baxevani, A., Cuzol, A., et al.: Spacetime models for moving fields with an application to significant wave height fields. Environmetrics 22, 354–369 (2011)
87. He, G.W., Zhang, J.B.: Elliptic model for space-time correlations in turbulent shear flows. Physical Review E 73, 055303 (2006)
88. Zhao, X., He, G.W.: Space-time correlations of fluctuating velocities in turbulent shear flows. Physical Review E 79, 046316 (2009)
89. He, X., He, G., Tong, P.: Small-scale turbulent fluctuations beyond Taylors frozen-flow hypothesis. Physical Review E 81, 065303 (2010)
90. Luding, S.: Introduction to discrete element methods: Basic of contact force models and how to perform the micro-macro transition to continuum theory. European Journal of Environmental and Civil Engineering 12, 785–826 (2008)
91. Sun, S., Shen, H.H.: Simulation of pancake ice load on a circular cylinder in a wave and current field. Cold Regions Science and Technology 78, 31–39 (2012)
92. Zhao, X., Shen, H.H.: Numerical simulation of gravity waves in viscous and viscoelastic materials. In: Proceedings of the 7th International Symposium on Environmental Hydraulics 2014 ISEH VII, Jan. 7–9, Singapore (2014)