海冰动力学的混合拉格朗日-欧拉数值方法

综合考虑欧拉坐标下有限差分法(FDM)在海冰动力学计算中的效率,以及拉格朗日坐标下光滑质点流体动力学方法(SPH)对海冰流变行为的精确模拟,本文发展了一种海冰动力学的混合拉格朗日-欧拉(HLE)数值方法。该方法首先在拉格朗日坐标下将海冰离散为若干个具有厚度、密集度的海冰质点,并由这些海冰质点通过Gauss函数对欧拉网格上的海冰参量进行积分插值;然后,在欧拉坐标下对海冰动量方程进行差分计算以确定各网格节点的海冰速度,并由此采用Gauss函数积分插值出拉格朗日坐标下各海冰质点的速度分布;最后,通过对海冰质点运动和分布的计算,确定出各海冰质点的位置、厚度和密集度等参量。采用该HLE方法对规则区域内的海冰堆积过程和涡动风场作用下的海冰动力演化趋势进行了数值试验;最后,采用该HLE方法对渤海海冰的动力过程进行了72h数值模拟,其计算结果与卫星遥感图像和现场观测资料吻合较好。以上计算结果均表明该HLE方法在海冰动力学数值模拟中具有较高的计算效率和模拟精度,可用于海冰动力过程的数值模拟。     

Modified PIC Method for Sea Ice Dynamics

The sea ice cover displays various dynamical characteristics such as breakup, rafting, and ridging under external forces. To model the ice dynamic process accurately, the effective numerical modeling method should be established. In this paper, a modified particle-in-cell （PIC） method for sea ice dynamics is developed coupling the finite difference （FD） method and smoothed particle hydrodynamics （SPH）. In this method, the ice cover is first discretized into a series of lagrangian ice particles which have their own sizes, thicknesses, concentrations and velocities. The ice thickness and concentration at Eulerian grid positions are obtained by interpolation with the Gaussian function from their surrounding ice particles. The momentum of ice cover is solved with FD approach to obtain the Eulerian cell velocity, which is used to estimate the ice particle velocity with the Gaussian function also. The thickness and concentration of ice particles are adjnsted with particle mass density and smooth length, which are adjusted with the redistribution of ice particles. With the above modified PIC method, numerical simulations for ice motion in an idealized rectangular basin and the ice dynamics in the Bohai Sea are carried out. These simulations show that this modified PIC method is applicable to sea ice dynamics simulation.     

Amodified discrete element model for sea ice dynamics

Considering the discontinuous characteristics of sea ice on various scales,a modified discrete element model（DEM） for sea ice dynamics is developed based on the granular material rheology.In this modified DEM,a soft sea ice particle element is introduced as a self-adjustive particle size function.Each ice particle can be treated as an assembly of ice floes,with its concentration and thickness changing to variable sizes under the conservation of mass.In this model,the contact forces among ice particles are calculated using a viscous-elastic-plastic model,while the maximum shear forces are described with the Mohr-Coulomb friction law.With this modified DEM,the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths.The thicknesses,concentrations and velocities of ice particles are obtained,and then reasonable dynamic process is analyzed.The sea ice dynamic process is also simulated in a vortex wind field.Taking the influence of thermodynamics into account,this modified DEM will be improved in the future work.     

冰动力学的拉格郎日离散元模式

本文描述一种应用于河冰和海冰动力学研究的平滑质点流体力学的离散元模式。该离散元方法是一种自由拉格郎日方法,和传统的欧拉网格数值方法相比,它具有较小的数值扩散并且能够更加灵活地处理复杂的冰过程等许多优点。本文首先给出海冰动力学的离散元模式的基本方法,并与欧拉有限差分方法和半拉格郎日的质点一网格方法进行了对比,其次,本文还给出了离散元海冰模式在渤海的一个应用。     

海冰动力过程的改进离散元模型及在渤海的应用

海冰的断裂、重叠和堆积等离散分布特性广泛地存在于极区和副极区的不同海域,并对海冰的生消、运移过程有着重要影响。针对海冰在不同尺度下的离散分布特点,发展海冰动力过程的离散元方法有助于完善海冰数值模式,提高海冰数值模拟的计算精度。为此,本文针对海冰生消运移过程中的非连续分布和形变特性,发展了适用于海冰动力过程的改进离散元模型(MDEM)。不同于传统离散元方法,该模型将海冰离散为具有一定厚度、尺寸和密集度的圆盘单元。海冰单元设为诸多浮冰块的集合体,其在运移和相互接触碰撞过程中,依照质量守恒发生单元尺寸、密集度和厚度的相应变化。基于海冰离散性和流变性的特点,该模型采用黏弹性接触本构模型计算单元间的作用力,并依据Mohr-Coulomb准则计算海冰法向作用下的塑性变形及切向摩擦力。为验证该模型的可靠性,本文对海冰在规则水域内的运移和堆积过程进行了分析,离散元计算结果与解析值相一致;此外,对旋转风场下海冰漂移规律的模拟进一步验证了本文方法的精确性。在此基础上,对渤海辽东湾的海冰动力过程进行了48h数值分析,计算结果与卫星遥感资料和油气作业区的海冰现场监测数据吻合良好。在下一步工作中将考虑海冰离散元模拟中的热力因素影响,发展具有冻结、断裂效应的海冰离散元模型,更精确地模拟海冰动力-热力耦合作用下的生消和运移过程。     

A viscoelastic-plastic constitutive model with Mohr-Coulomb yielding criterion for sea ice dynamics

A new viscoelastic-plastic （VEP） constitutive model for sea ice dynamics was developed based on continuum mechanics. This model consists of four components： Kelvin-Vogit viscoelastic model, Mohr-Coulomb yielding criterion, associated normality flow rule for plastic rehololgy, and hydrostatic pressure. The numerical simulations for ice motion in an idealized rectangular basin were made using smoothed particle hydrodynamics （SPH） method, and compared with the analytical solution as well as those based on the modified viscous plastic（VP） model and static ice jam theory. These simulations show that the new VEP model can simulate ice dynamics accurately. The new constitutive model was further applied to simulate ice dynamics of the Bohai Sea and compared with the traditional VP, and modified VP models. The results of the VEP model are compared better with the satellite remote images, and the simulated ice conditions in the JZ20-2 oil platform area were more reasonable.     

普里兹湾及其邻近海区冰-海相互作用的数值研究 Ⅰ.模式

南大洋在全球气候系统中起着重要的作用,对世界大洋水团的形成有重要的影响。在世界大洋中,约有55%-60%的海水特性应当归结于南大洋的物理过程。目前,南大洋的研究已得到各国海洋学者的日益关注,进展较大。但是,对于地处印度洋扇形区的普里兹湾海区的观测和研究则相对较少,其结果的差别甚大。例如底层水形成问题,有些研究者认为这一海区的底层水主要来源于威德尔海和罗斯海,本区内对底层水的贡献即使有,也是非常小的(Smith et al.,1984; Mantyla et al.,1995)。而有些研究者则从观测资料中找到了底层水有可能形成的迹象。就目前研究的结果来看,有些年份,如1982年(Middleton et al.,1989),1987年(Woehler et al.,1988),1991年(乐肯堂等,1996)均发现了异常高盐的陆架水,它有可能与深层水混合而形成底层水。对于该海区的环流特别是深层环流迄今为止也是知之甚少。大多数研究是基于动力高度的计算结果( Grigor yev,1967;Smith et al.,1984,1993;Middleton et al.,1989),但他们给出的环流型式相互之间差异很大。这些差异的存在,虽然确有年际变化等因素,但也不能排除研究方法本身的局限。该海区地形复杂(图1),海冰有显著的季节变化和年际变化(Allison et al.,1993,1994),使得该海区的物理海洋状况非常复杂。南极地区由于环境恶劣,海洋观测集中在夏季,并且资料的连续性较差,因而使传统的研究方法受到很大限制。为了充分发挥有限的实测资料的作用,采用合理的动力学和热力学模式并利用数值方法求解模式方程,不失为一种有效的研究途径。迄今为止,这一海区的数值研究还很少,考虑热力学作用的模式则尚未见诸报道。本文将利用最新的资料和模式,并在模式中同时考虑动力学和热力学的作用,用以研究普里兹湾海区的环流与海冰的动力学和热力学过程。以往的研究发现、等密面分析是研究普里兹湾海区混合与环流的有效方法(乐肯堂等,1997),我们将采用国际上新近发展起来的一种基于等密面的数值计算模式,研究普里兹湾海区环流和海冰的季节变化。这一工作将有助于进一步解决该海区南极底层水的形成问题,因而对于深入认识该海区在南大洋环流系统以至全球气候系统中的作用有重要意义。     

锥体导管架海洋平台冰激振动的DEM-FEM耦合分析及高性能算法

在寒区海域,冰荷载是影响海洋平台安全运行的主要环境荷载之一,由其引起的冰激振动给平台结构及其上部设备带来了严重危害。为分析不同冰况下平台的振动响应,本文建立了导管架海洋平台冰激振动的离散元（DEM）-有限元（FEM）耦合模型。采用具有黏接-破碎性能的等粒径球体离散单元对海冰的破碎特性进行模拟,通过由梁单元构建的海洋平台有限元模型获得结构的振动响应。在离散元与有限元的接触区域中实现了两个模型间计算参数的传递。为提高该耦合模型的计算效率和规模,发展了基于动力子结构方法的DEM-FEM耦合模型。为验证该耦合模型的有效性和可行性,将不同冰况下得到的冰荷载与ISO19906和JTS 144-1-2010标准进行了对比。结果表明,计算得到的冰荷载与标准相近,且冰厚与冰荷载呈二次非线性关系。同时,从冰速和冰厚两方面对比了渤海四桩腿JZ20-2 MUQ锥体导管架平台冰激振动加速度的数值结果和现场实测数据,发现冰速与振动加速度呈线性关系,冰厚与振动加速度呈二次非线性关系,并且振动加速度与冰速和冰厚平方的乘积呈线性关系。     

Numerical simulation for dynamical processes of sea ice

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Application of an accurate advection algorithm to sea-ice modelling

Modern numerical sea-ice models contain detailed parameterizations of dynamic and thermodynamic processes affecting ice distribution and thickness. However, nearly all such models advect sea ice in response to wind and ocean forcing using either upstream or centered-difference methods, whose deficiencies are well known. We describe application of the second-order moment advection scheme of Prather [J. Geophys. Res. 91 (1986) 6671]. In idealized tests this method produces relatively distinct ice edges while maintaining positive ice thicknesses and concentrations. Sensitivity of an Arctic circulation model forced by climatological data is described.     

寒潮天气下高风险冰块追踪预测方法及数值模拟

为向拟建、在建和已建冰区所有冷源取水工程海域的海冰环境监测和动态风险预警提供技术支撑,本文构建了海冰–海洋耦合条件下的拉格朗日粒子追踪预测模型,并以辽东湾某核电站取水口为例,模拟并探讨了寒潮天气下高风险冰块在24 h、48 h和72 h的运移轨迹及其进入取水口的概率。结果表明,由于取水口的走向与流向和风向几乎垂直,因此在口门外随机释放的1 200个高风险冰块粒子中只有不到6%的粒子进入到取水口内。通过分区域标识粒子颜色,发现这些粒子多来自于靠近取水口300 m范围内。敏感性分析的结果表明,当释放粒子数量增至5倍时,结论不变。该项研究为冷源取水安全预警提供了一种新方法。     

Discrete elementmodeling of ice loads on ship hulls in broken ice fields

Ice loads on a ship hull affect the safety of the hull structure and the ship maneuvering performance in ice-covered regions. A discrete element method （DEM） is used to simulate the interaction between drifting ice floes and a moving ship. The pancake ice floes are modelled with three-dimensional （3-D） dilated disk elements considering the buoyancy, drag force and additional mass induced by the current. The ship hull is modelled with 3D disks with overlaps. Ice loads on the ship hull are determined through the contact detection between ice floe element and ship hull element and the contact force calculation. The influences of different ice conditions （current velocities and directions, ice thicknesses, concentrations and ice floe sizes） and ship speeds are also examined on the dynamic ice force. The simulated results are compared qualitatively well with the existing field data and other numerical results. This work can be helpful in the shil3 structure design and the navigation securitv in ice-covered fields.     

海冰动力学过程的数值模拟

讨论了海冰动力学性质并阐述决定海冰漂移的动量平衡,冰脊和水道形成及确定冰应力与形变、强度之间关系的海冰流变学.提出了模拟海冰动力学过程的数值模式,模式中冰厚分布由开阔水、平整冰和堆积冰3种要素表示.在这3要素的预报方程中引入形变函数,采用一种参数化方法模拟冰脊和水道.为了表示冰内相互作用,将海冰作为一种非线性粘性可压缩物质,采用粘-塑性本构关系.本文还概述和讨论了模式中所采用的数值方法,应用此模式模拟了渤海、波罗的海的波的尼亚湾和拉布拉多海的冰漂移.渤海冰漂移模拟结果明显地显示出潮周期变化,还模拟了渤海的冰脊和水道,进行了海冰流变学参数的敏感性试验.并将此冰模式与大气模式和边界层模式联接,给出渤海海冰预报结果.     

渤海海冰漂移数值研究

本文利用海冰－海洋动力耦合模式对渤海典型天气形势下海冰动力过程作了数值模拟，海冰模式建立在动量和质量守恒基础上，忽略了海冰变化的热力过程。海冰厚度被划分为三类：堆积冰、平整冰和开阔冰，冰的形变由一个厚度的重新分布约束条件确定。海洋模式是一个二维风暴潮模式．同时考虑了潮汐的作用。风场资料来自于沿岸气象观测站每日四次的风观测，计算网格是十分之一经纬度。主要的分析和模拟是在大气和海洋共同作用下海冰的漂流特点。观测结果比较表明，数值模拟结果基本上反映了该海域流冰的漂移性质，同时也可为短期冰情预报提供有益的参考。     

海冰模式和数值预报

根据渤海冰情,在海冰动力学和热力学研究基础上,提出一种海冰动力一热力模式。该模式包括平整冰、堆积冰和开阔水三要素,采用粘一塑性本构关系计算冰内应力。利用参数化方法处理变形函数和热力增长率。该冰模式与潮流模式耦合研究渤海冰－潮相互作用,并与ＥＣＯＭ－Ｓｉ海洋模式耦合进行预报试验。该冰模式与大气模式联接,或应用气象部门数值天气预报产品进行海冰业务数值预报。本文还给出了预报结果。     

基于Mohr-Coulomb准则的黏弹-塑性海冰动力学本构模型

针对中小尺度下海冰动力作用过程中的漂移、重叠和堆积特征,在连续介质力学基础上建立了一个黏弹塑性海冰动力学本构模型.该模型主要包括四部分,即海冰在屈服前的Kelvin Vogit黏弹模型、海冰塑性屈服的Mohr Coulomb准则、屈服后相关联的正交流动法则和影响海冰强度的静水压力.采用黏弹塑性本构模型对规则海域内的海冰堆积过程进行了数值试验,其结果与传统黏塑性模型、改进的黏塑性模型和经典冰坝理论的解析解相符,可合理地模拟海冰堆积的动力过程.为进一步检验该黏弹塑性本构模型的适用性,对渤海海冰的动力过程进行了48h的数值模拟,计算结果与海冰卫星遥感现场观测资料一致.通过与传统的黏塑性和改进的黏塑性模型结果的对比分析,进一步验证了黏弹塑性模型在中小尺度海冰动力学模拟中的可靠性.在以上海冰堆积的数值试验和渤海海冰动力学模拟中均采用了光滑质点流体动力学(SPH)方法.     

Improvement of short-term sea ice forecast in the southern Okhotsk Sea

In this study, a numerical model of 7-day forecast of sea ice produced by the Japan Meteorological Agency was improved by the following approaches. First, a new ice dynamic model was introduced: the distributed mass/discrete floe model. The model takes account of discrete characteristics of ice floes and well simulates the ice edge location at low computational cost. Secondly, the grid size was reduced to 5 × 5 km for the future high resolution forecasts. Next, the sea surface current data was examined because it significantly influences sea ice movement. We applied two new datasets of HINO and Okhotsk Ocean General Circulation Model (Okhotsk OGCM), which are estimated by numerical simulations, for the 7-day forecast of sea ice. Ice southward speed in January and the whorl formations in February and March were well reproduced with Okhotsk OGCM datasets. Finally, the ocean heat flux at the ice-ocean interface was refined. As a result, we achieved an ice edge error reduction from 30.8 km to 23.5 km.     

海洋工程引发的悬浮物扩散预测模型优化

在详细了解工程附近海域自然状况的基础上,基于雷诺平均的Navier-Stokes方程组模拟该海域的水动力状况,采用有限体积数值格式离散水动力学方程。在此基础上,引入该海域附近两个建设工程的影响,基于对流扩散的水质模型模拟悬浮物浓度场的分布状况,并分别计算了两个工程对海域的影响程度,即影响贡献度。通过实测数据验证了模型的准确性和实用性。经过结果分析可知,工程2对控制点的影响较工程1的影响贡献度系数小65%左右,这主要是由于工程1相对于工程2距离湾顶更近,水深较浅,海流速度较小,海水交换能力较差,扩散能力也较弱造成的。     

螺旋桨对海冰切削作用的DEM-FEM耦合分析

当船舶在冰区航行时,螺旋桨会与海冰相互碰撞并导致桨叶的变形和损坏,进而影响船舶的航行安全。为研究海冰与螺旋桨的相互作用过程,采用离散元(DEM)—有限元(FEM)耦合方法构建海冰—螺旋桨切削模型。海冰和螺旋桨模型分别采用具有黏结—破碎特性的球体离散单元和8节点六面体有限单元构造。基于该DEM-FEM耦合模型讨论了不同切削深度下,螺旋桨所承受冰载荷的特点和规律;最后,研究了螺旋桨切削海冰过程中进速系数、推力系数、扭矩系数之间的对应关系,并讨论了海冰—螺旋桨相互作用过程中冰压力、Mises应力和变形的分布特点。以上研究可为寒区船舶安全航行和螺旋桨设计提供有益的参考。     

A coupled ice–ocean model for the Greenland,Iceland and Norwegian Seas

Simulations from a coupled ice–ocean model that highlight the importance of synoptic forcing on sea-ice dynamics are described. The ocean model is a non-hydrostatic primitive equation model coupled to a dynamic thermodynamic sea ice model. The ice modelling sensitivity study presented here is part of an ongoing research programme to define the role played by sea ice in the energy balance of the Greenland Sea. The different categories of sea ice found in the subpolar regions are simulated through the use of equations for thin ice, thick ice and the Marginal Ice Zone. A basin scale numerical model of the Greenland, Iceland and Norwegian Seas has a horizontal resolution of 20 km and a vertical grid spacing of 50 m. This resolution is adequate for resolving the mesoscale topographic structures known to control the circulation in this region. The spin-up reproduces the main features of the circulation, including the cyclonic gyres in the Norwegian and Greenland Basins and Iceland Plateau. Topographic steering of the flow is evident. The baroclinic Rossby radius of deformation is between 5 and 10 km so that the model is not eddy-resolving. The coupled ice–ocean model was run for a period of two weeks. The influence of horizontal resolution of the atmospheric model was tested by comparing simulations using six hourly wind fields from the ECMWF with those generated using six hourly fields from a HIRLAM, with horizontal resolutions of 1° and 0.18° respectively. The simulations show reasonable agreement with satellite ice compactness data and data of ice transports across sections at 79°N, 75°N and Denmark Strait.