海冰离散元模型的研究回顾及展望

doi:10.3724/SP.J.1084.2012.00315

摘要/Abstract

摘要： 为描述极区及副极区海冰在不同尺度下的离散分布特性，以及海冰与海洋结构相互作用过程中的破碎性能，海冰的离散单元模型从上世纪80年代发展起来并不断完善。本文将海冰离散单元模型分为地球物理尺度( ~100km)、浮冰块尺度(10m ~ 10km)和海洋结构尺度(1m ~ 100m)等三种不同尺度，讨论了不同尺度下海冰的离散分布规律或海冰由连续状态向离散状态转化的动力过程。通过对块体、圆盘和颗粒不同形态的海冰离散单元模型的介绍，对其在极区海冰的动力特性、海冰重叠堆积及其与波浪的作用过程、海冰与海洋结构的相互作用中的应用进行了分析，对海冰强度的尺度效应进行了讨论。最后，讨论了海冰离散单元模型中存在的问题和重点研究内容。

关键词: 海冰, 离散单元模型, 尺度效应

Abstract: In order to describe the discrete nature of sea ice at different scales, sea ice discrete element models have been developed since 1980s. In this study, three scales of sea ice are divided as geophysical scale (~100km), floe scale (~10km) and structure scale (1m~100m). On each scale, the discrete distribution and dynamic process from continuous to discrete state of sea ice are presented. Sea ice discrete element models in terms of blocks, disks and particles are introduced, and their application in dynamic characteristics of sea ice in polar regions, simulation of sea ice rafting and ridging and the interaction with wave, interaction between sea ice and structures, and sea ice mechanical properties modeling are analyzed. Sea ice strength due to scale effect is discussed. Finally, future studies on sea ice discrete element models are suggested.

Key words: sea ice, discrete element models, scale effect

季顺迎李春花刘煜. 海冰离散元模型的研究回顾及展望[J]. 极地研究, 2012, 24(4): 315-330.

JI Shunying，LI Chunhua，LIU Yu. A REVIEW OF ADVANCES IN SEA-ICE DISCRETE ELEMENT MODELS[J]. ADVANCES IN POLAR SCIENCE, 2012, 24(4): 315-330.

参考文献

1. Shen H H, Hibler W D, Lepparanta M. On applying granular flow theory to a deforming broken ice field. Acta Mechanics, 1986, 63: 143-160.

2. Shen H H, Hibler W D, Lepparanta M. The role of floe collisions in sea ice rheology. Journal of Geophysical Research, 1987, 92(C10): 7085-7096

3. Lu Q M, Larsen J, Tryde P. On the role of ice interaction due to floe collisions in marginal ice zone dynamics. Journal of Geophysical Research, 1989, 94: 14525-14537.

4. Lepparanta M, Lensu M, Lu Q M. Shear flow of sea ice in the Marginal Ice Zone with collision rheology. Geophysica, 1990, 25(1-2):57-74.

5. Loset S. Discrete element modeling of a broken ice field-Part II: simulation of ice loads on a boom Cold Regions Science and Technology, 1994, 22:349-360.

6. Hopkins M A. On the mesosacle interaction of lead ice and floes. Journal of Geophysical Research, 1996a, 101(C8): 18315-18326

7. Hopkins M A. Four stages of pressure ridging. Journal of Geophysical Research, 1998,103: 21883-21891

8. Dai M, Shen H H, Hopkins M A, Ackley S F. Wave rafting and the equilibrium pancake ice cover thickness. Journal of Geophysical Research, 2004, 109(C07023): 1-9.

9. Shen H H, Ackley S F, Yang Y. Limiting diameter of pancake ice. Journal of Geophysical Research, 2004, 109(C12-35): 1-10.

10. Hopkins M A, Frankenstein S, Thorndike A S. Formation of an aggregate scale in Arctic sea ice. Journal of Geophysical Research, 2004c, 109(C01032):1-10

11. Wilchinsky A V, Feltham D L. Modelling the rheology of sea ice as a collection of diamond-shaped floes. Journal of Non-Newtonian Fluid Mechanics, 2006a, 138: 22–32

12. Selvadurai A P S, Sepehr K. Two-dimensional discrete element simulations of ice-structure interaction. Interactional Journal of Solids and Structures, 1999, 36:4919-4940.

13. Lau M, Lawrence K P, Rothenburg L. Discrete element analysis of ice loads on ships and structures. Ships and Offshore Structures, 2011, 6(3): 211–221.

14. Lepparanta M. The drift of sea ice. Praxis Publishing, Chichester UK, 2004.

15. Dempsey J P. Research trends in ice mechanics. International Journal of Solids and Structures, 2000, 37: 131-153.

16. Sanderson T J O. Ice mechanics-risks to offshore structures. Graham and Trotman, London, 1988.

17. Weiss J. Fracture and fragmentation of ice: a fractal analysis of scale invariance. Engineering Fracture Mechanics, 2001, 68: 1975-2012.

18. Stern H L, Lindsay R W. Spacial scaling of Arctic sea ice deformation. Journal of Geophysical Research, 2009, 114(C10), doi:10.1029/2009JC005380

19. Davis N R, Wadhams P. A statistical analysis of Arctic pressure ridge morphology. Journal of Geophysical Research, 1995, 100(C6): 10915-10926.

20. Weiss J, Schulson E, Stern H. Sea ice rheology from in-situ, satellite and laboratory observations: fracture and friction. Earth and Planetary Science Letters, 2007, 255:1-8.

21. Schulson E M. Compressive shear faults within arctic sea ice: Fracture on scales large and small. Journal of Geophysical Research, 2004, 109(C07016): 1-23.

22. Korsnes R, Souza S R, Donangelo R, et al. Scaling in fracture and refreezing of sea ice. Physica A, 2004, A, 331:291-196.

23. Hopkins M A, Tuhkuri J, Lensu M. Rafting and riding of thin ice sheets. Journal of Geophysical Research, 1999a, 104(C6): 13605-13613.

24. Flato G M, Hibler W D. Ridging and Strength in modeling the thickness distribution of Arctic sea ice. Journal of Geophysical Research, 1995, 100(C9): 18611-18626

25. Wilchinsky AV, Feltham D L, Hopkins M A. Effect of shear rupture on aggregate scale formation in sea ice.Journal of Geophysical. Research, 2010, 115(C10), C10002, doi:10.1029/2009JC006043

26. Wilchinsky A V, Feltham D L, Hopkins M A. Modelling the reorientation of sea-ice faults as the wind changes direction. Annals of Glaciology, 2011, 52(57): 83-90.

27. Hopkins M A. A discrete element Lagrangian sea ice model. International Journal for Computer-Aided Engineering, 2004, 21(2-3):409-421

28. Hopkins M A, Thorndike A S. Floe formation in Arctic sea ice. Journal of Geophysical Research, 2006, 111, C11S23, doi:10.1029/2005JC003352

29. Hibler W D. Sea ice fracturing on the large scale. Engineering Fracture Mechanics, 2001, 68: 2013-2043

30. Sedlacek J, Lemieux J F, Mysak L A, Tremblay L B, Holland D M. The granular sea ice model in spherical coordinates and its application to a global climate model. Journal of Climate, 2007, 20: 5946-.5961.

31. Wichinsky A V, Feltham D L. Anisotropic model for granulated sea ice dynamics. Journal of the Mechanics and Physics of Solids, 2006b, 54:1147-1185.

32. Feltham D L. Granuar flow in the marginal ice zone. Philosophical Transactions of the Royal Society A, 2005, 363: 1677-1700.

33. Feltham D L. Sea ice rheology. Annual Review of Fluid Mechanics, 2008, 40:91-112.

34. Shunying Ji, Anliang Wang, Baohui Li, Yu Liu, Hai Li. A modified discrete element model for sea ice dynamics. Proceedings of the 21st International Conference on Port and Ocean Engineering under Arctic Conditions, 2011, Montreal, Canada.

35. 季顺迎, 沈洪道, 王志联, 奚海莉, 岳前进. 基于Mohr-Coulomb准则的粘弹塑性海冰动力学本构模型. 海洋学报, 2005, 27(4): 19-30.

36. Shen H T, Chen Y C, Wake A, et al. Lagrangian discrete parcel simulation of river ice dynamics. International Journal of Offshore and Polar Engineering, 1993, 3(4): 328-332.

37. Flato G M. A Particle-in-cell Sea-ice Model. Atmosphere and Oceanography. 1993, 31(3): 339- 358.

38. Tin T, Jeffries M O. Morphology of deformed first-year ice features in the Southern Ocean. Cold Regions and Technology, 2003, 36: 141-163.

39. Marchenko A, Makshtas A. A dynamic model of ice ridge buildup. Cold Regions Science and Technology, 2005, 41: 175-188.

40. Hopkins M A, Tuhkuri J. Compression of floating ice fields. Journal of Geophysical Research, 1999, 104(C7): 15815-15825

41. Shiraswa K, Lepparanta M, Saloranta T, et al. The thickness of coastal fast ice in the Sea of Okhotsk. Cold Regions Science and Technology, 2005, 42: 25-40.

42. Lepparanta M, Lensu M, Kosloff P, Veitch B. The life story of a first-year sea ice ridge, Cold Regions Science and Technology, 1995, 23:279-290.

43. Lipscomb, W H, Hunke E C, Maslowski W, et al. Ridging, strength, and stability in high-resolution sea ice models,Journal of Geophysical Research, 2007, 112, C03S91, doi:10.1029/2005JC003355

44. Ovsienko S. Numerical modeling of the drift of ice. Izvestiya, Atmospheric and Oceanic Physics, 1976, 12(11):1201-1206.

45. 王昕，雷瑞波，孔祥鹏，李志军，张勇. 辽东湾近岸堆积冰表面形态特征分析. 海洋通报, 2008, 27(5): 18-22.

46. Hopkins M A, Hibler W D, Flato G M. On the numerical simulation of the sea ice ridging process. Journal of Geophysical Research, 1991, 96(C3):4809-4820

47. 王永学, 李春花, 孙鹤泉, 李志军. 斜坡式防波堤前海冰堆积数值模拟. 水利学报, 2003, 6:105-110.

48. 李春花, 王永学, 李志军, 孙鹤泉. 半圆型防波堤前海冰堆积模拟. 海洋学报, 2006, 28(4): 172-177.

49. Hoyland K V. Morphology and small-scale strength of ridges in the North-western Barents Sea. Cold Regions Science and Technology, 2007, 48:169-187.

50. Hopkins M A. Discrete element modeling with dilated particles. Engineering Computations, 2004, 21:422-430.

51. Hopkins M A. On the ridging of intact lead ice. Journal of Geophysical Research, 1994, 99(C8):16351-16360

52. Dumont D, Kohout A, Bertino L. A wave‐based model for the marginal ice zone including a floe breaking parameterization. Journal of Geophysical Research, 2011,116, C04001, doi:10.1029/ 2010JC006682

53. Hansen E H, Loset S. Modelling floating offshore units moored in broken ice: model description. Cold Regions Science and Technology, 1999, 29:97-106.

54. Hansen E H, Loset S. Modelling floating offshore units moored in broken ice: comparing simulaions with ice tank tests. Cold Regions Science and Technology, 1999, 29:107-119.

55. Hopkins M A, Shen H H. Simulation of pancake-ice dynamics in wave field. Annals of Glaciology, 2001, 33: 355 -360.

56. Shen H H. Validation of the DEM Application for Pancake Ice Using STAR-CCM+. Report of American Bureau of Shipping, 2011.

57. Xu Z, Tartakovsky A M, Pan W. Discrete-element model for the interaction between ocean waves and sea ice. Physical Review E, 2012, 85: 016703.

58. Jordaan I. Mechanics of ice-structure interaction. Engineering Fracture Mechanics, 2001, 68: 1923- 1960.

59. Qu Yan, Yue Qianjin, Bi Xiangjun, Karna Tuomo. A random ice force model for narrow conical structures. Cold Regions Science and Technology, 2006, 45: 148-157.

60. Arenson L U. Numerically modelling the strength of ice using discrete elements. Proceedings of the 2nd PFC Symposium, 2004, Kyoto, Japan.

61. Polojarvi A, Tuhkuri J. 3D discrete numerical modelling of ridge keek punch through tests. Cold Regions Scienc and Technology, 2009, 56:18-29.

62. Lau M. Discrete element modeling of ship manoeuvring in ice. Porceedigns of the 18th IAHR Interaction Symposium on Ice, 2006, 25-32.

63. 季顺迎. 非均匀颗粒介质的类固-液相变行为及其本构模型. 力学学报, 2007, 39(2):223-237.

64. Babic M, Shen H H, Shen H T. The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations. J. Fluid Mech., 1990, 219: 81~118

65. Itasca Consulting Group, Particle Flow Code in 3 Dimensions, Online Manual, 2004.

66. 季顺迎, 狄少丞, 李正,等. 海冰与直立结构相互作用的离散单元数值模拟, 工程力学, 2011(已录用).

67. Konuk I, Gurtner A, Yu S. Study of dynamic ice and cylindrical structure interaction by the cohesive element method. Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions. 2009, Lulea, Sweden.

68. Konuk I, Gurtner A, Yu S. A Cohesive Element Framework for Dynamic Ice–Structure Interaction Problems Part I: Review and Formulation: Proceedings of 28th Internaional Conference on Ocean, Offshoreand Arctic Engineering, Honolulu, USA, 2009b, OMAE2009-79262.

69. Girard L, Weiss J, Molines J M, et al. Evaluation of high-resolution sea ice models on the basis of statistical and scaling properties of Arctic sea ice drift and deformation. Journal of Geophysical Research, 2009, 114: C08015.

70. Girard L, Bouillon S, Weiss J, et al., A new modeling framework for sea-ice mechanics based on elasto-brittle rheology, Annals of Glaciology, 2011, 52(57): 123-132.

71. Schulson E M, Fortt A L, Iliescu D, Renshaw C E. Failure envelope of fisr-year Arctic sea ice: the role of friction in compressive fracture. Journal of Geophysical Research, 2006, 111: C11S25.

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