Radiation and Diffraction of Water Waves by a Submerged Body with Ice Cover in Finite Depth

This paper presents the three-dimensional Green-function method to predict the radiation and diffraction of water waves by a submerged body in water of uniform finite depth with an ice cover. The fluid is assumed to be perfect and irrotational, the ice is modelled as an elastic plate. The zero-speed Green function of finite depth satisfying the linearized covered-surface condition is derived in three dimensions, the numerical results for the Green function and its derivatives are given. The integral equations are established by distributing the source strength on the body surface, the radiation and diffraction problems are solved. A submerged sphere is taken as an example, the effects of the water depth and the flexural rigidity of ice cover on hydrodynamics are analysed, and the good agreement with the analytical solutions reveals that the present method is correct and reliable.

     

Influence of ice conditions on the effectiveness of the resonant method of breaking ice cover by submarines

This paper describes a numerical model for analyzing the stress-strain state of ice cover which has fractures of various widths caused by hydrodynamic loads due to submarine motion. Calculations and experiments were performed using the model of unbreakable ice, and the results were used to obtain dependences of the amplitude of deflections and stress in ice cover on the width of the ice fracture. The behavior of ice cover under wave loading was studied.     

水下成组药包爆炸作用下冰盖动态响应数值模拟

利用大型有限元软件ANSYS/LS-DYNA建立了成组药包水下爆炸冰盖动态响应模型,通过数值计算,得到了冲击波峰值压力变化规律,峰值压力与理论计算结果基本吻合。本文分析了冰盖在成组药包水下爆炸冲击载荷下的应力分布及垂直位移响应特征。结果表明,冰盖迎爆面为压缩破坏,背爆面为拉伸破坏,两者数值均十分接近,其中迎爆面最大压力值可达18.12MPa,冰盖近爆炸点最大垂直位移为1.211cm,两药包连线中点最小位移为0.15cm,达到脆性冰盖形成贯通裂隙的基本条件,从而确定了冰盖在水下成组药包大间距布设条件下,其动态破坏形式是以产生裂隙为主要特征。     

Ice cover perturbation by a dipole in motion within a liquid

The two-dimensional problem of ice cover perturbation by a dipole starting to move uniformly, rectilinearly, and horizontally in a liquid initially at rest is considered. It is shown that stationary waves of two different types can be established on the liquid/ice interface, depending on the ice thickness and the dipole velocity. Examples of the numerical investigation of these waves are presented.     

基于多介质、多尺度离散元方法的冰载荷数值冰水池

极地船舶与海洋工程结构冰载荷的确定是其结构抗冰设计、冰区安全运行和结构完整性管理的重要研究内容. 当前快速发展的高性能计算技术和多介质、多尺度数值方法为准确、高效地计算结构冰载荷提供了有效的途径, 其中以离散元方法为代表的数值方法取得了出色的研究成果. 为此, 本文针对目前极地船舶与海洋工程结构对冰载荷及力学响应的工程需求, 同时考虑国内外对海冰、工程结构与流体相互耦合的多介质、多尺度数值方法研究现状, 对极地船舶与海洋工程数值冰水池的概念、框架、开发技术以及基于离散元方法的软件实现与工程应用进行了论述. 数值冰水池在船舶与海洋工程结构冰载荷确定方面具有可靠性、经济性、快速性、扩展性和情景化等显著优势. 本文工作借鉴数值水池的研究思路, 以典型船舶和海洋平台结构冰载荷及结构力学响应的离散元计算为例, 探讨了数值冰水池研究的可行性和工程应用前景, 阐述其与理论分析、现场测量和模型试验研究相结合的必要性. 以上研究有益于中国在极地船舶与海洋工程领域形成具有独立知识产权的数值计算分析平台, 对中国极地海洋强国的战略实施具有很好的启发和指导意义.      

海冰动力学数值模拟中改进的PIC方法

为了准确地模拟海冰的动力过程,需要建立精确有效的数值方法。本文结合质点网格法(PIC)和光滑质点流体动力学方法(SPH)发展了一种改进的PIC方法。该方法在欧拉坐标下对海冰动量方程进行差分计算,在拉格朗日坐标下进行海冰质点位移、厚度和密集度计算,并采用Gauss函数进行欧拉网格点与拉格朗日质点间海冰参数的交互插值。采用改进的PIC方法对规则区域内的海冰堆积过程进行了数值试验,对渤海海冰的动力过程进行了72小时数值模拟。计算结果均表明改进的PIC方法具有计算量小,计算结果平稳精确的优点,可很好地适用于海冰动力作用过程的数值模拟。     

水位变化对正倒锥体冰载荷影响的离散元分析

在海冰与锥体海洋结构的相互作用过程中,潮汐水位变化时海冰作用于锥体结构的位置改变对冰载荷具有显著影响.本文采用具有粘结破碎功能的离散元方法计算海冰与锥体作用的破坏过程.同时考虑海冰上下表面温度差异对海冰强度的影响,将离散元计算冰载荷及海冰破坏模式与渤海现场实测数据进行对比验证.离散元结果表明,海冰与正锥和倒锥碰撞时均发生弯曲破坏,且冰载荷均随水线处锥径的增大而增大.在水线处锥径相同的情况下,正锥冰载荷大于倒锥冰载荷,而正锥作用下海冰的断裂长度则较小.基于离散元计算结果和渤海现场观测资料分析了海冰与正锥、倒锥作用时冰载荷和断裂长度差异的主要原因.海冰与正倒锥交界线处作用时,一般发生弯曲破坏.当冰层中心高度与正倒锥交界线的高度相同时,海冰才会发生局部挤压破碎,但冰荷载并没有明显升高.由此可见,倒锥体结构可有效降低冰载荷从而具有较好的抗冰性能.以上研究表明离散元方法可确定海冰与锥体结构作用时的海冰破碎规律和冰载荷特性,为海洋工程结构的抗冰设计提供参考依据.      

河渠冰水力学研究进展和趋势

从河渠冰水力学基本理论7个方面(水热循环机理、流冰形成输移扩散机理、锚冰岸冰形成发展释放、封河冰塞机理、开河冰坝机理、水工建筑物冰塞机理、水冰沙互馈作用机理)、河渠冰情预测预报及过程模拟、河冰关键参数观测技术与装备等层面介绍了国内外的河冰水力学研究的主要进展和动向,剖析了当前科学研究和工程应用研究中存在的难题,并从理论...     

Action of periodic surface pressure on an ice cover in the vicinity of a vertical wall

This paper presents the solution of the linear hydroelastic problem for steady forced vibrations of a semi-infinite ice cover under the effect of localized external load. The ice cover is simulated by a viscoelastic thin plate, the thickness of the fluid layer is assumed to be small, and the shallow water theory is used. The fluid is limited by a solid vertical wall, and the rectilinear edge of the elastic plate adjacent to the wall can be both free and clamped. The solution is obtained with the help of the Fourier integral transform. The behavior of the ice cover is studied depending on the frequency of the external load and boundary conditions on the edge of the plate. It is shown that, in the case of a free edge of the plate, there are considerable deflections on the edge, which could be comparable with deflections at the center of the pressure impact region. It is established that, due to the existence of wave movements of the type of edge waves, the external load energy is transferred to larger distances along the free edge, and there are significant bending moments on the edge of the clamped plate, which can lead to fracture of the ice cover with sufficiently great intensity of the external load.     

Estimates of the effective compressive strength

One problem encountered when determining the effective mechanical properties of large-scale objects, which requires calculating their strength in processes of mechanical interaction with other objects, is related to the possible variability in their local properties including those due to the action of external physical factors. Such problems comprise the determination of the effective strength of bodies one of whose dimensions (thickness) is significantly less than the others and whose properties and/or composition can vary with the thickness. A method for estimating the effective strength of such bodies is proposed and illustrated with example of ice cover strength under longitudinal compression with regard to a partial loss of the ice bearing capacity in deformation. The role of failure localization processes is shown. It is demonstrated that the proposed approach can be used in other problems of fracture mechanics.     

喜马拉雅山东南地区地质灾害发育规律初步研究

利用遥感手段,结合MapGis,研究了喜马拉雅山东南地区地质灾害的发育情况,发现本区发育的主要地质灾害有滑坡、崩塌、泥石流、冰湖以及堰塞湖。其中崩塌、滑坡、泥石流斜坡地质灾害是本区最重要的地质灾害类型,占到总灾害数量的95.3%。在此基础上对喜马拉雅山东南地区地质灾害发育规律初步研究,发现本区地质灾害的发育在空间上的分布并非均匀,而是具有丛集性的特点。滑坡灾害主要发育在隆子和朗县。泥石流灾害比较严重的有米林、隆子和洛扎3县,而崩塌则主要集中在隆子县。研究发现,本区滑坡发育与地层、地形坡度以及土地类型关系密切,其中修康群、日当组和念青唐古拉群是本区的"易滑地层"。涅如组由于面积大,其中发育的滑坡较多,但是滑坡的发育率只略高于本区的平均水平。统计表明,16°～30°的坡度范围是滑坡最容易发生的。大于45°以上的坡段很少发生滑坡。灌木林和天然草地这两种土地类型滑坡发育率最高。对于泥石流,研究表明,涅如组中泥石流发育面积最大,发育率也最高。泥石流发育的最适宜坡度也是16°～30°这样一个坡度范围。冰川和永久积雪区则最易发生泥石流。崩塌发育与地层类型、坡度的关系较为密切,崩塌主要发育在涅如组中,并且集中在坡度大于60°以上的陡坡段中。这些初步成果的取得,是以后进行该区地质灾害空间预测的基础。     

Numerical modelling of ice jam resistance to main channel flow

In northern countries, subfreezing temperatures during the winter season result in the formation of ice covers on most rivers. Towards the end of the winter season, during the spring break-up period, stationary ice covers become weak in strength and break up. The resulting broken ice pieces or ice floes are significantly larger in thickness and have a rougher undersurface relative to sheet ice and impose higher hydraulic resistance. The downstream movement of the ice floes may be arrested under conditions such as an intact ice cover, bridge piers or channel constrictions, among others, thereby initiating a break-up ice jam. These ice jams most often have been observed to cause very high water stages. Detrimental effects caused by these high water levels encompass those of operational and design-related problems such as the flooding of communities due to ice-jam-induced backwater, flood risk assessments, altering of the open water flow regime, bed scour and flooding of bridges. The ability to predict the influence of an ice jam on the main flow is of considerable importance in river engineering and can be viewed upon by its effects on the variation in the water surface levels. All other information is dependent on the foregoing. The ice jam influence on the main flow can be regarded with respect to local and global standpoints. The primary objective of this study is to formulate the influence of the ice jam on the main channel flow. The formulation is then coupled with a two-dimensional numerical model for the simulation of the water flow regime. The data from different laboratory experiments on ice jams are reproduced numerically. Various simulations are then carried out to compute the water surface levels and velocities in channels under ice jam conditions. The numerical results are then compared with the laboratory data. Results show that the mathematical formulation developed to predict the water surface levels and velocities along the ice jam length as well as upstream and downstream of its leading and trailing edges respectively gives satisfactory predictions.     

Modeling ocean wave propagation under sea ice covers

Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as: landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice,brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermal-mechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover: mass loading,thin elastic plate, and viscous layer models. From physical arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a continuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelastic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms,the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology. Laboratory experiments,field measurements and numerical simulations supporting the fundamental research in wave-ice interaction models are discussed. We conclude with some outlook of future research needs in this field.     

Zone of superficial damage arising from the explosion of a large meteorite in the air

A numerical investigation into the zone of superficial damage attributable to the explosion of a large meteorite in the air over the earth's surface is presented. The results are applied to the case of the explosion of the Tungus cosmic body.     

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.     

Oscillations of a cylindrical body submerged in a fluid with ice cover

The linear plane problem of oscillations of an elliptic cylinder in an ideal incompressible fluid of finite depth in the presence of an ice cover of finite length is solved. The ice cover is modeled by an elastic plate of constant thickness. The hydrodynamic loads acting on the body are determined as functions of the oscillation frequency and the positions of the cylinder and plate.     

Interaction of surface and flexural-gravity waves in ice cover with a vertical wall

The problem of the interaction of surface and flexural-gravity waves with a vertical barrier is solved in a two-dimensional formulation. It is assumed that the fluid is ideal and incompressible, has infinite depth, and is partially covered with ice. The ice cover is modeled by an elastic plate of constant thickness. The eigenfrequencies and eigenmodes of oscillation of the floating elastic ice plate, the deflection and deformation of ice, and the forces acting on the wall are determined.     

An experimental study on the interactions between surface waves and floating viscoelastic covers

A possible mathematical ice model for the wave interactions in polar seas was developed based on the assumption that an ice cover behaved as a Voigt viscoelastic material. The dispersion relation was found to depend on the rheological properties of the cover. In the present study, an experimental approach was developed that can enable the verification of the theoretical predictions in the laboratory. The approach utilized the blended mixture of white oil and Polydimethylsiloxane (PDMS) material with various mass percentages of a curing agent, to create a floating layer with a range of targeted viscoelastic properties. Due to the large coverage required for wave flume experiments, special curing procedures were also established for the preparation of PDMS material. The rheological results showed that the mechanical behavior of the floating cover was close to a Voigt material. Experiments were conducted to analyze the wave interactions with the floating viscoelastic cover. The measured data showed an obvious change of wavelength when waves propagated along the cover region. It is observed that the change in wavelength can be linked quantitatively to the viscoelastic properties based on the numerical predictions by Wang and Shen (2010). Some differences were however noted for less viscous covers under longer wave periods. A direct comparison of the PDMS covers with a polypropylene (PP) cover was also performed for verification. Only wave lengthening was observed under the PP cover. With a shear modulus more than three orders of magnitude greater than that of PDMS, the theoretical wavelength for the PP cover from Wang and Shen (2010) is very close to that of the thin elastic plate theory from Fox and Squire (1990). Comparison between these two theoretical results and the measured data again deviated with longer wave periods. In both PDMS and PP cases, edge effects and pitching motion of the covers were present at various degrees. In addition, the materials were not strictly a Voigt type. The small deviation from the idealized rheological behavior could also contribute to differences between theoretical and experimental results.     

移动载荷作用下浮冰的非线性动力学响应

本文考虑非线性、惯性和阻尼的影响, 研究了任意深度二维理想流体顶部浮冰的振动. 对相关的拟微分算子进行展开并将非线性项保留至三阶后, 完全非线性问题被简化为仅与自由面上的变量相关的三阶截断模型. 为了验证简化模型的准确性, 重点关注了自由孤立波解. 在不考虑阻尼的情况下, 采用多重尺度方法推导了三阶非线性薛定谔方程(NLS), 利用该方程预测了任意水深下原始欧拉方程中自由波包型孤立波解的存在性及三阶截断模型的准确性. 相比于Dinvay等所提出的二阶模型, 三阶截断模型的优势在于其对应的三阶NLS具有准确的非线性项系数, 能够在最小相速度附近更好地模拟冰层的动力学响应. 进一步地对自由孤立波解进行数值计算, 数值结果表明三阶截断模型在分岔曲线和孤立波波形上均与完全欧拉方程吻合良好, 准确性高于二阶截断模型. 基于三阶截断模型, 探究了匀速局域化载荷作用下的浮冰非线性动力学响应并将时间依赖解与实验测量数据进行比较, 数值计算结果与实验记录吻合良好.      

GPU-BASED DISCRETE ELEMENT MODELLING OF INTERACTION BETWEEN SEA ICE AND JACK-UP PLATFORM STRUCTURE

在海冰与自升式海洋平台结构的相互作用过程中,冰载荷是影响平台结构振动响应和疲劳寿命的重要因素. 采用具有粘接-破碎效应的离散元模型,可对海冰与自升式海洋平台结构作用中的海冰破碎特征及相应冰载荷进行数值分析. 针对自升式海洋平台的多桩腿结构特性及其冰载荷离散元分析的大规模计算需求,建立了基于GPU 的并行算法并开发了相应的计算程序. 为实现离散元分析的高效计算,采用网格排序方法创建单元邻居列表,以快速确定海冰单元间及其与平台结构间的接触模式和作用力. 此外,还发展了球体单元与圆柱形结构在不同接触形式下的计算模型. 为检验该离散元模型的有效性,对渤海锥体海洋平台结构的作用过程进行了计算,并与现场实测冰力数据进行了对比验证. 在此基础上对多桩腿自升式平台结构的冰载荷进行了离散元分析,获得了海冰的破坏特性,确定了不同桩腿上的冰力时程. 该模型可进一步应用于不同类型海洋结构的冰载荷分析,为冰区海洋平台的结构设计和现役平台结构的疲劳分析提供参考依据.