海冰与波流耦合动力学的研究进展

倪宝玉; 曾令东; 熊航; 吴其远

doi:10.6052/0459-1879-20-394

海冰与波流耦合动力学的研究进展

doi: 10.6052/0459-1879-20-394

哈尔滨工程大学船舶工程学院,哈尔滨 150001

基金项目: 1) 国家重点研发计划(2017YFE0111400);国家自然科学基金(51979051);国家自然科学基金(51979056);国家自然科学基金(51639004);黑龙江省自然科学基金(A2018003)

详细信息

作者简介:
2) 倪宝玉,教授,主要研究方向：冰水船耦合动力学. E-mail: nibaoyu@hrbeu.edu.cn

通讯作者:
倪宝玉

中图分类号: U661.1
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- 被引次数: 0
出版历程
- 收稿日期: 2020-11-22
- 刊出日期: 2021-03-10

REVIEW ON THE INTERACTION BETWEEN SEA ICE AND WAVES/CURRENTS

College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China

摘要

摘要: 随着全球气候变暖,北极活动频次的逐渐增加,海冰与波流的耦合作用成为了国内外的热点研究问题. 海冰的存在会改变波浪的传播特性和色散关系,也会改变海流运动的边界条件,使得海流在冰面下边界处可能产生漩涡脱落等现象;而海冰在波浪、海流等动力作用下,也会不断发生生消、断裂、重叠和堆积等动力学行为.海冰与波流耦合动力学中存在几大难点问题：一是海冰模型的构建,需要针对海冰类型和性质的不同,考虑不同区域的海冰分布情况建立合适的海冰模型.二是冰水之间的耦合问题,海冰边界影响着冰水之间的动量和能量交换,对于冰盖、浮冰等不同类型海冰,需分别处理边界问题;冰水耦合引起的海冰破坏,其破坏模式也是多样的.三是波流联合场的构建,目前尚无较好的方法构建波流联合场,导致海冰与波流联合场作用的相关研究仍极其匮乏.因此,本文针对海冰与波流相互作用问题,回顾和讨论国内外对海冰与波浪、海冰与海流及海冰与波流相互作用的研究现状和技术难点,展望了未来可以进一步深入研究的问题,提出了初步的思路以供参考.
- 海冰 /
- 波浪 /
- 海流 /
- 耦合作用 /
- 海冰模型
Abstract: With global warming and the increasing frequency of Arctic activities, the interaction between sea ice and waves/currents has become an attractive research issue at home and abroad. The existence of sea ice changes the propagation characteristics and dispersion relationships of waves, and also changes the boundary conditions of ocean currents, inducing vortex shedding at the lower surface of the sea ice. The sea ices generate and extinct, fracture, overlap and accumulate under the effects of waves and currents. There are several difficulties in studying the interaction between sea ice and waves/currents. The first is the construction of sea ice model appropriately, which needs to consider the differences of the types and properties of sea ice in different cold regions. The distributions of sea ice also should be taken into account in the sea ice model. The second is the coupling problem between sea ice and water. The boundary of sea ice affects the exchange of momentum and energy between sea ice and water. The boundary conditions of sea ice should be dealt with appropriately in terms of ice sheet and ice floes. There are many fracture modes of sea ice, but the sea ice may have complex fracture modes with coexistence of many different fracture modes under the action of sea ice and water coupling. The third is the construction of wave-current joint field. At present, there is no efficient method to construct the wave-current joint field, which leads to lack of relevant research on interaction for sea ice and wave-current joint field to understand the physic problem. Therefore, this paper reviews and discusses the research status and technical difficulties of interactions between sea ice and wave, current and wave-current fields. The problems that can be further studied in the future are predicted and the preliminary ideas are put forward for reference.
- sea ice /
- wave /
- ocean current /
- coupling /
- sea ice model

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参考文献(104)

[1]	卢景美, 邵滋军, 房殿勇, 等. 北极圈油气资源潜力分析. 资源与产业, 2010,12(4):29-33 (Lu Jingmei, Shao Zijun, Fang Dianyong, et al. Analysis of oil-gas resources potential in the arctic circle. Resource & Industries, 2010,12(4):29-33 (in Chinese))
[2]	寿建敏. 我国极地航运能力建设和高冰级船队发展对策分析. 极地研究, 2018,30(4):419-428 (Shou Jianmin. Analysis on the construction of China's polar shipping capacity and countermeasures for the development of high ice class fleet. Chinese Journal of Polar Research, 2018,30(4):29-33 (in Chinese))
[3]	Ni BY, Han DF, Di SC, et al. On the development of ice-water-structure interaction. Journal of Hydrodynamics, 2020,32(4):629-652
[4]	刘璐, 尹振宇, 季顺迎. 船舶与海洋平台结构冰载荷的高性能扩展多面体离散元方法. 力学学报, 2019,51(6):1720-1739 (Liu Lu, Yin Zhenyu, Ji Shunying. High-performance dilated polyhedral based DEM for ice loads on ship and offshore platform structures. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1720-1739 (in Chinese))
[5]	龙雪, 刘社文, 季顺迎. 水位变化对正倒锥体冰载荷影响的离散元分析. 力学学报, 2019,51(1):74-84 (Long Xue, Liu Shewen, Ji Shunying. Influence of water level on ice load on upward-downward conical structure based on DEM analysis. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):74-84 (in Chinese))
[6]	Squire VA. Of ocean waves and sea ice. Annual Review of Fluid Mechanics, 2003,27(1):115-168
[7]	Squire VA. Of ocean waves and sea-ice revisited. Cold Regions Science and Technology, 2007,49(2):110-133
[8]	Squire VA. Past present and impendent hydroelastic challenges in the polar and subpolar seas. Philosophical Transactions of The Royal Society A, 2011,369:2813-2831
[9]	Squire VA. Ocean wave interactions with sea ice: A reappraisal. Annual Review of Fluid Mechanics, 2020,52(1):37-60
[10]	Zhao X, Shen HH, Cheng S. Modeling ocean wave propagation under sea ice covers. Acta Mechanica Sinica, 2015,31(1):1-15
[11]	Shen HH. Modelling ocean waves in ice-covered seas. Applied Ocean Research, 2019,83:30-36
[12]	Peters AS. The effect of a floating mat on water waves. Communications on Pure and Applied Mathematics, 1950,3(4):319-354
[13]	Weitz M, Keller JB. Reflection of water waves from floating ice in water of finite depth. Communications on Pure and Applied Mathematics, 1950,3(3):305-318
[14]	Wadhams P. The Seasonal Ice Zone, the Geophysics of Sea Ice. US: Springer, 1986: 825-991
[15]	Hosking RJ, Sneyd AD, Waugh DW. Viscoelastic response of a floating ice plate to a steadily moving load. Journal of Fluid Mechanics, 2006,196(1):409-430
[16]	Keller JB. Gravity waves on ice covered water. Journal of Geophysical Research: Oceans( 1978-2012), 1998,103(C4):7663-7669
[17]	Carolis DG, Desiderio D. Dispersion and attenuation of gravity waves in ice: A two layer viscous fluid model with experimental data validation. Physics Letters A, 2002,305(6):399-412
[18]	Wang R, Shen HH. Gravity waves propagating into an ice covered ocean: A viscoelastic model. Journal of Geophysical Research}: Oceans (1978-2012), 2010,115:C06024
[19]	Zhao X, Cheng S, Shen HH. Nature of wave modes in a coupled viscoelastic layer over water. Journal of Engineering Mechanics, 2017,143(10):04017114
[20]	Zhao X, Shen HH. Three-layer viscoelastic model with eddy viscosity effect for flexural-gravity wave propagation through ice cover. Ocean Modelling, 2018,131:15-23
[21]	Zhao X, Zhang CP. A theoretical model of the Wind-wave growth over an ice-covered sea. Boundary Layer Meteorology, 2021,178:1-19
[22]	Cheng SK, Rogers WE, Thomson J, et al. Calibrating a viscoelastic sea ice model for wave propagation in the arctic fall marginal ice zone. Journal of Geophysical Research-Oceans, 2017,122(11):8770-8793
[23]	Cheng SK, Tsarau A, Evers KU, et al. Floe size effect on gravity wave propagation through ice covers. Journal of Geophysical Research-Oceans, 2019,124(1):320-334
[24]	赵欣. 海浪模式中海冰弹性模量计算的理论方法//第十四届全国环境力学学术会议论文集, 大连, 2018-08-5-7 (Zhao Xin. A theoretical method for calculating the elastic modulus of sea ice in wave models//Proceedings of the 14th National Conference on Environmental Mechanics, Dalian, 2018-08-5-7 (in Chinese))
[25]	Meylan MH, Bennetts LG, Peter MA. Water-wave scattering and energy dissipation by a floating porous elastic plate in three dimensions. Wave Motion, 2016:S0165212516300695
[26]	Zheng S, Meylan MH, Fan L, et al. Wave scattering by a floating porous elastic plate of arbitrary shape: A semi-analytical study. Journal of Fluids and Structures, 2019,92:102827
[27]	Chen H, Gilbert RP, Guyenne P. Dispersion and attenuation in a porous viscoelastic model for gravity waves on an ice-covered ocean. European Journal of Mechanics-B/Fluids, 2019,78:88-105
[28]	Balmforth NJ, Craster RV. Ocean waves and ice sheets. Journal of Fluid Mechanics, 1999,395:89-124
[29]	Fox C, Squire VA. Reflection and transmission characteristics at the edge of shore fast sea ice. Journal of Geophysical Research Oceans, 1990,95(C7):11629-11639
[30]	Fox C, Squire VA. On the oblique reflexion and transmission of ocean waves at shore fast sea ice. Philosophical Transactions of the Royal Society A Mathematical Physical & Engineering Sciences, 1994,347:185-218
[31]	Tkacheva LA. Hydroelastic behavior of a floating plate in waves. Journal of Applied Mechanics & Technical Physics, 2001,42(6):991-996
[32]	Tkacheva LA . The diffraction of surface waves by a floating elastic plate at oblique incidence. Journal of Applied Mathematics & Mechanics, 2004,68(3):425-436
[33]	Sahoo T, Yip TL, Chwang AT. Scattering of surface waves by a semi-infinite floating elastic plate. Physics of Fluids, 13(11):3215-3222
[34]	Linton CM, Chung H. Reflection and transmission at the ocean/sea-ice boundary. Wave Motion, 2003,38:43-52
[35]	Zhao X, Shen HH. Ocean wave transmission and reflection between two connecting viscoelastic ice covers: An approximate solution. Ocean Modelling, 2013,71(7):102-113
[36]	Zhao X, Shen HH. Ocean wave transmission and reflection by viscoelastic ice covers. Ocean Modelling, 2015,92:1-10.
[37]	Barrett MD, Squire VA. Ice-coupled wave propagation across an abrupt change in ice rigidity, density, or thickness. Journal of Geophysical Research Oceans, 1996,101(C9):20825-20832
[38]	Evans DV, Porter R. Wave scattering by narrow cracks in ice sheets floating on water of finite depth. Journal of Fluid Mechanics, 2003,484:143-165
[39]	Porter R, Evans DV. Scattering of flexural waves by multiple narrow cracks in ice sheets floating on water. Wave Motion, 2006,43(5):425-443
[40]	Porter R, Evans DV. Diffraction of flexural waves by finite straight cracks in an elastic sheet over water. Journal of Fluids & Structures, 2007,23(2):309-327
[41]	Li ZF, Wu GX, Shi YY. Wave diffraction by a circular crack in an ice sheet floating on water of finite depth. Physics of Fluids, 2018,30(11):117103
[42]	Li ZF, Wu GX, Ren K. Wave diffraction by multiple arbitrary shaped cracks in an infinitely extended ice sheet of finite water depth. Journal of Fluid Mechanics, 2020,893:A14
[43]	Marchenko AV. Resonance interactions of waves in an ice channel. Journal of Applied Mathematics & Mechanics, 1997,61(6):931-940
[44]	Chung H, Linton CM. Reflection and transmission of waves across a gap between two semi-infinite elastic plates on water. The Quarterly Journal of Mechanics and Applied Mathematics, 2005,58(1):1-15
[45]	Shi YY, Li ZF, Wu GX. Wave excited motion of a body floating on water confined between two semi-infinite ice sheets. Physics of Fluids, 2019,31(6):067111
[46]	Williams TD, Squire VA. Scattering of flexural--gravity waves at the boundaries between three floating sheets with applications. Journal of Fluid Mechanics, 2006,569:113-140
[47]	Porter R. Trapping of waves by thin floating ice floes. The Quarterly Journal of Mechanics and Applied Mathematics, 2018,71(4):463-483
[48]	Korobkin AA, Khabakhpasheva TI, Papin AA. Waves propagating along a channel with ice cover. European Journal of Mechanics, 2014,47:166-175
[49]	Khabakhpasheva TI, Batyaev EV. Hydroelastic waves in a channel covered with a free ice sheet. Fluid Dynamics, 2015,50(6):775-788
[50]	Ren K, Wu GX, Li ZF. Hydroelastic waves propagating in an ice-covered channel. Journal of Fluid Mechanics, 2020,886(A18):1-24
[51]	Zeng LD, Korobkin AA, Ni BY, et al. Hydroelastic waves propagating in a shallow fluid contained in a channel covered by two ice sheets of finite width//25th IAHR International Symposium on Ice, Trondheim, 2020-11-23-25
[52]	Meylan M, Squire VA. Finite-floe wave reflection and transmission coefficients from a semi-infinite model. Journal of Geophysical Research Oceans, 1993,98(C7):12537-12542
[53]	Meylan M, Squire VA. The response of ice floes to ocean waves. Journal of Geophysical Research, 1994,99(C1):891-900
[54]	Meylan MH, Squire VA. Response of a circular ice floe to ocean waves. Journal of Geophysical Research: Oceans, 1996,101(C4):8869
[55]	Meylan MH. Wave response of an ice floe of arbitrary geometry. Journal of Geophysical Research Oceans, 2002,107(C1):3005
[56]	Wand CD, Meylan MH. A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate. Journal of Fluids and Structures, 2004,19(4):557-572
[57]	Bennetts LG, Williams TD. Wave scattering by ice floes and polynyas of arbitrary shape. J Fluid Mech, 2010,662:5-35
[58]	Porter R. The coupling between ocean waves and rectangular ice sheets. Journal of Fluids and Structures, 2019,84:171-181
[59]	Bai W, Zhang T, Mcgovern DJ. Response of small sea ice floes in regular waves: A comparison of numerical and experimental results. Ocean Engineering, 2017,129:495-506
[60]	倪宝玉, 刘晨辉, 胡文进, 等. 二维Stokes波与多块浮冰相互作用数值模拟. 水动力学研究与进展(A辑), 2019,34(2):141-148 (Ni Baoyu, Liu Chenhui, Hu Wenjin, et al. Numerical simulation on the interaction between two-dimensional Stokes wave and multiple ice floes. Chinese Journal of Hydrodynamics (A), 2019,34(2):151-148 (in Chinese))
[61]	倪宝玉, 叶昱图, 胡文进, 等. 浮冰在Stokes波作用下运动响应研究. 华中科技大学学报(自然科学版), 2020,48(10):75-80 (Ni Boayu, Ye Yutu, Hu Wenjin, et al. Study on motion response of ice floe under Stokes wave. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2020,48(10):75-80 (in chinese))
[62]	Meylan MH, Bennetts LG, Cavaliere C, et al. Experimental and theoretical models of wave-induced flexure of a sea ice floe. Physics of Fluids, 2015,27(4):1-7
[63]	郭春雨, 宋妙妍, 骆婉珍, 等. 海冰在波浪中纵向运动的试验研究. 华中科技大学学报(自然科学版), 2017,45(6):85-90 (Guo Chunyu, Song Miaoyan, Luo Wanzhen, et al. Experimental study on longitudinal motion of sea ice in waves. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2017,45(6):85-90 (in Chinese))
[64]	Sree DK, Law AWK, Shen HH, et al. An experimental study on the interactions between surface waves and floating viscoelastic covers. Wave Motion, 2017,70:195-208
[65]	Masson D, Leblond P H. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. Journal of Fluid Mechanics, 2006,202:43-81
[66]	Meylan MH, Masson D. A linear Boltzmann equation to model wave scattering in the marginal ice zone. Ocean Modelling, 2006,11(3):417-427
[67]	Bennetts LG, Squire VA. Wave scattering by multiple rows of circular ice floes. Journal of Fluid Mechanics, 2009,639:213-238
[68]	Bennetts LG, Squire VA. Linear wave forcing of an array of axisymmetric ice floes. Ima Journal of Applied Mathematics, 2010,75(1):108-138
[69]	Peter MA, Meylan MH. Water-wave scattering by vast fields of bodies. Siam Journal on Applied Mathematics, 2009,70(5):1567-1586
[70]	Bennetts LG, Peter MA, Squire VA, et al. A three-dimensional model of wave attenuation in the marginal ice zone. Journal of Geophysical Research Oceans, 2010,115:C12043
[71]	Montiel F, Squire VA, Bennetts LG. Attenuation and directional spreading of ocean wave spectra in the marginal ice zone. Journal of Fluid Mechanics, 2016,790:492-522
[72]	Montiel F, Squire VA, Bennetts LG. Evolution of directional wave spectra through finite regular and randomly perturbed arrays of scatterers. SIAM Journal on Applied Mathematics, 2015,75(2):630-651
[73]	Meylan MH, Bennetts LG. Three-dimensional time-domain scattering of waves in the marginal ice zone. Philosophical Transactions of the Royal Society A Mathematical Physical & Engineering Sciences, 2018,376(2129):20170334
[74]	Bennetts L, Williams T. Water wave transmission by an array of floating disks. Proceedings of the Royal Society A Mathematical Physical & Engineeringences, 2015,471(2173):20140698
[75]	Zhao X, Shen HH. A diffusion approximation for wave scatterings by randomly distributed ice floes. Ocean Modeling, 2016,107:21-27
[76]	陈晓东, 崔海鑫, 王安良, 等. 基于巴西盘试验的海冰拉伸强度研究. 力学学报, 2020,52(3):625-634 (Chen Xiaodong, Cui Haixin, Wang Anliang, et al. Experimental study on sea ice tensile strength based on Brazilian tests. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(3):625-634 (in Chinese))
[77]	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, 2011,116:C04081
[78]	Williams TD, Bennetts LG, Squire VA, et al. Wave-ice interactions in the marginal ice zone. Part 1: Theoretical foundations. Ocean Modelling, 2013,71:81-91
[79]	Williams TD, Bennetts LG, Squire VA, et al. Wave-ice interactions in the marginal ice zone. Part 2: Numerical implementation and sensitivity studies along 1D transects of the ocean surface. Ocean Modelling, 2013,71:92-101
[80]	Williams TD, Rampal P, Bouillon S. Wave-ice interactions in the neXtSIM sea-ice model. The Cryosphere, 2017,11:2117-2135.
[81]	Zhang JL, Schweiger A, Steele M, et al. Sea ice floe size distribution in the marginal ice zone: Theory and numerical experiments. Journal of Geophysical Research: Oceans, 2015,120(5):3484-3498
[82]	王永学, 李广伟, 李春花, 等. 波浪作用下海冰断裂的试验研究. 自然科学进展, 2000,10(6):549-553 (Wang Yongxue, Li Guangwei, Li Chunhua, et al. Experimental study on sea ice fracture under wave action. Progress in Natural Science, 2000,10(6):549-553 (in Chinese))
[83]	http://www.hsva.de.
[84]	Ni BY, Chen ZW, Zhong K, et al. Numerical simulation of a polar ship moving in level ice based on a one-way coupling method. Journal of Marine Science and Engineering, 2020,8(9):692
[85]	孙惠, 卢鹏, 李志军. 冰下流场动力学特性的数值模拟研究. 数学的实践与认识, 2015,45(3):69-77 (Sun Hui, Lu Peng, Li Zhijun. Numerical simulation on dynamic characteristics of flow field under ice. Journal of Mathematics in Practice and Theory, 2015,45(3):69-77 (in Chinese))
[86]	Hibler WD. A dynamic thermodynamic sea ice mode. Journal of Physical Oceanography, 1979,9(4):815-846
[87]	Hunke EC, Dukowicz JK. An elastic--viscous--plastic model for sea ice dynamics. Journal of Physical Oceanography, 1997,27(9):1849-1867
[88]	季顺迎, 沈洪道, 王志联, 等. 基于Mohr-Coulomb准则的黏弹-塑性海冰动力学本构模型. 海洋学报, 2005(4):19-30 (Ji Shunying, Shen Hongtao, Wang Zhilian, et al. A viscoelastic-plastic constitutive model with Mohr-Coulomb yielding criterion for sea ice dynamics. Acta Oceanologica Sinica, 2005(4):19-30 (in Chinese))
[89]	李海, 季顺迎, 沈洪道, 等. 海冰动力学的混合拉格朗日-欧拉数值方法. 海洋学报, 2008,30(2):1-11 (Li Hai, Ji Shunying, Shen Hongtao, et al. A hybrid Lagrangian-Eulerian numerical model for sea ice dynamics. Acta Oceanologica Sinica, 2008,30(2):1-11 (in Chinese))
[90]	季顺迎, 王安良, 米丽丽, 等. 海冰动力过程的改进离散元模型及在渤海的应用. 海洋学报, 2015,37(5):54-67 (Ji Shunying, Wang Anliang, Mi Lili, et al. Modified discrete element model for sea ice dynamics and its applications in the Bohai Sea. Acta Oceanologica Sinica, 2015,37(5):54-67 (in Chinese))
[91]	孙惠. 冰底形态对流场特性影响的数值模拟研究. [硕士论文]. 大连: 大连理工大学, 2014 (Sun Hui. Numerical simulation on the influence of ice bottom morphology on flow field. [Master Thesis]. Dalian: Dalian University of Technology, 2014 (in Chinese))
[92]	吴岩. 冰脊对冰下流场影响的数值模拟研究. [硕士论文]. 大连: 大连理工大学, 2016 (Wu Yan. Numerical simulation on the influence of ice ridges on flow field under ice. [Master Thesis]. Dalian: Dalian University of Technology, 2016 (in Chinese))
[93]	王军. 初始冰塞厚度与水流条件及冰流量关系的试验研究. 水利水运工程学报, 1999(4):385-389 (Wang Jun. A study on the relationship about initial ice jam thickness with its stream conditions and ice discharge. Hydro-Science and Engineering, 1999(4):385-389 (in Chinese))
[94]	王军. 平衡冰塞厚度与水流条件和冰流量关系的试验研究. 兰州大学学报(自然科学版), 2002,38(1):117-121 (Wang Jun. A study on the relations about balance ice jam thickness with its flow conditions and ice discharge. Journal of Lanzhou University(Natural Sciences) 2002,38(1):117-121 (in Chinese))
[95]	李志军, 贾青, 董吉武, 等. 冰对水工结构物作用力的物理模拟. 中国水论坛, 2010: 217-225 (Li Zhijun, Jia Qing, Dong Jiwu, et al. Physical simulation of the force of ice on hydraulic structures. China Water Forum, 2010: 217-225 (in Chinese))
[96]	李志军, 贾青, 王国玉, 等. 流冰对码头排桩撞击力的物理模拟试验研究. 工程力学, 2010,27(3):169-173 (Li Zhijun, Jia Qing, Wang Guoyu, et al. Physical simulation of ice floe impact forces on pile structres of wharfs. Engineering Mechanics, 2010,27(3):169-173 (in Chinese))
[97]	张强. PIV技术在实验室模拟冰下流场测试中的应用. [博士论文]. 大连: 大连理工大学, 2009 (Zhang Qiang. Application of PIV on flow field measurement under floe ice in laboratory modeling. [PhD Thesis]. Dalian: Dalian University of Technology, 2009 (in Chinese))
[98]	Pite HD, Topham DR, Van HBJ. Laboratory measurements of the drag force on a family of two-dimensional ice keel models in a two-layer flow. Journal of Physical Oceanography, 1995,25(12):3008-3031
[99]	McPhee MG. Advances in understanding ice ocean stress during and since AIDJEX. Cold Regions Science & Technology, 2012, 76-77-24-36
[100]	吴甜宇, 邱文亮, 胡哈斯. 海冰与波流联合作用下深水基础桥梁动力反应分析. 武汉理工大学学报(交通科学与工程版), 2018,42(6):930-936 (Wu Tianyu, Qiu Wenliang, Hu Hasi. Dynamic response analysis of deep water foundation bridge under combined action of sea ice and wave current. Journal of Wuhan University of Technology(Transportation Science & Engineering), 2018,42(6):930-936 (in Chinese))
[101]	Dolatshah A, Bennetts LG, Meylan MH, et al. An experimental model of wind-induced rafting of pancake ice floating on waves// 34th International Workshop on Water Waves and Floating Bodies, 2019, April 7-10, Newcastle, Australia
[102]	Bennetts LG, Yiew LJ, Meylan MH, et al. An experimental model of non-rafting collisions between ice floes caused by monochromatic water waves// 19th Australasian Fluid Mechanics Conference, 2014, April 8-11, Melbourne, Australia
[103]	Yiew LJ, Bennetts LG, Meylan MH, et al. Wave-induced collisions of thin floating disks. Physics of Fluids, 2018,29(12):127102
[104]	M?rtensson S, Meier HEM, Pemberton P, et al. Ridged sea ice characteristics in the Arctic from a coupled multicategory sea ice model. Journal of Geophysical Research Oceans, 2012, 117:C00D15