Ice response to an underwater body moving in a frozen channel

Strains in the ice cover of a frozen channel, which are caused by a body moving under the ice at a constant speed along the channel, are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is modeled by a thin viscoelastic plate clamped to the channel walls. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images without account for ice deflection in the leading order. The problem of a dipole moving in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of ice and the strains in the ice cover are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform along the channel, the method of normal modes across the channel, and the truncation method for resulting infinite systems of linear equations. It was revealed that the strains in the ice strongly depend on the speed of the dipole with respect to the critical speeds of the hydroelastic waves propagating along the frozen channel. The width of the channel matters even it is much larger than the characteristic length of the ice cover.     

Hydrodynamic Pressure of Liquid in the Process of Motion of a Region of Constant Disturbances over the Floating Ice Cover

We study the dependence of the hydrodynamic pressure induced in a liquid as a result of motion of a load of constant intensity over the floating ice cover on the flexural stiffness of ice and the character of distribution of the load over the moving region. The contribution of the deflection of ice in the vicinity of the load and the induced flexural and flexural-gravitational waves to the formation of the field of hydrodynamic pressure near the ice-water interface is estimated.__________Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 3–14, January–February, 2005.     

Wave Currents Generated by a Moving Load in a Liquid Covered with Ice

We study horizontal wave currents generated in a liquid of finite depth by a load of constant intensity moving over the floating ice cover and analyze the dependences of the space structure of the field of wave velocities on the characteristics of the ice cover and the velocity of motion of the load. It is shown that the velocity of wave currents caused by flexural waves can increase with the velocity of motion of the load, whereas the wave currents caused by the gravity waves decay monotonically. The ice compression increases the velocity of horizontal wave currents.     

Modelling of three-dimensional flexural oscillations of an ice cover induced by a moving load

Ice cover oscillations induced by a moving load are studied in a linear formulation using a threedimensional flexural-gravity wave model. Theoretically-derived ice deflection profiles and critical velocities of the moving vehicle are compared with known experimental data. Translated by V. Puchkin.     

Effect of ice cover on oscillations of fluid in a closed basin

Within the framework of the linear theory of long waves, the problem of the effect of ice cover on seiche oscillations of fluid in a two-dimensional constant-depth basin is solved. The eigenfrequencies and eigenfunctions of seiche oscillations are obtained for different boundary conditions at ice edges: rigid coupling and free edges. The forced oscillations of fluid and ice under the action of a moving disturbance of atmospheric pressure are investigated. The change in the stress of ice bending is considered and it is shown that the coast ice can be broken.     

The influence of the bottom contour on the deformed state of the ice cover due to the motion of the submarine

The authors have previously determined that the effectiveness and failure pattern of the ice cover caused by flexural-gravity waves generated by a submerged body motion near the bottom ice can greatly depend on the depth of the water area. In its turn, the presence of a ledge on the ice surface may affect a wave propagation pattern. This paper presents an experimental study of the bottom contour influence on the deflection and length of flexural-gravity waves. The authors describe a numerical model for the analysis of the deformed state of ice caused by hydrodynamic loads due to a submarine motion, taking into account the bottom contour. The experiments are carried out in the ice tank. The results of calculations and experiments are compared.     

The vertical mode method in the problems of flexural-gravity waves diffracted by a vertical cylinder

The linear three-dimensional problem of ice loads acting on a vertical circular cylinder frozen in an ice cover of infinite extent is studied. The loads are caused by an uni-directional hydroelastic wave propagating in the ice cover towards the cylinder mounted to the see bottom in water of constant depth. There are no open water surfaces in this problem. The deflection of the ice cover is described by the Bernoulli–Euler equation of a thin elastic plate of constant thickness. At the contact line between the ice cover and the surface of the cylinder, some edge conditions are imposed. In this study, the edge of the ice plate is either clamped to the cylinder or has no contact with the cylinder surface, with the plate edge being free of stresses and shear forces. The water is of finite constant depth, inviscid and incompressible. The problem is solved by both the vertical mode method and using the Weber integral transform in the radial coordinate. Each vertical mode corresponds to a root of the dispersion relation for flexural-gravity waves. It is proved that these two solutions are identical for the clamped edge conditions. This result is non-trivial because the vertical modes are non-orthogonal in a standard sense, they are linearly dependent, the roots of the dispersion relation can be double and even triple, and the set of the modes could be incomplete. A general solution of the wave-cylinder interaction problem is derived by the method of vertical modes and applied to different edge conditions on the contact line. There are three conditions of solvability in this problem. It is shown that these conditions are satisfied for any parameters of the problem.     

Interaction of uniform current with a circular cylinder submerged below an ice sheet

The problem of a uniform current passing through a circular cylinder submerged below an ice sheet is considered. The fluid flow is described by the linearized velocity potential theory, while the ice sheet is modelled through a thin elastic plate floating on the water surface. The Green function due to a source is first derived, which satisfies all the boundary conditions apart from that on the body surface. Through differentiating the Green function with respect to the source position, the multipoles are obtained. This allows the disturbed velocity potential to be constructed in the form of an infinite series with unknown coefficients which are obtained from the boundary condition. The result shows that there is a critical Froude number which depends on the physical properties of the ice sheet. Below this number there will be no flexural waves propagating to infinity and above this number there will be two waves, one on each side of the body. When the depth based Froude number is larger than 1, there will always be a wave at far upstream of the body. This is similar to those noticed in the related problem and is different from that in the free surface problem without ice sheet. Various results are provided, including the properties of the dispersion equation, resistance and lift, ice sheet deflection, and their physical features are discussed.     

Ship waves in a continuously stratified basin with ice cover

Ship waves generated in an exponentially stratified fluid when an axisymmetrical area of pressure of constant intensity moves over a floating ice cover are studied in a linear statement. The influence of ice rigidity on the distribution of amplitudes of the internal wave disturbances along the constant phase lines is analysed.Translated by Mikhail M. Trufanov.     

Sea ice evolution and internal wave generation due to a tidal jet in a frozen sea

The purpose of this study is to investigate the influence of tidal currents on sea ice in Spitsbergen fjords which may cause rapid decrease of the ice thickness due to erosion and melting of the ice. The effect was studied in-situ near the narrow channel connecting the Van Mijen Fjord and Lake Vallunden. The strong jet-like tidal currents in the strait driven by semidiurnal tide continue into the lake preventing ice freezing along a narrow strip during high tide and relatively warm weather. Understanding the formation of open water regions or regions with thin ice is important for the safe transportation on ice. We estimate conditions and representative time over which strong tidal current influences ice thickness along a narrow strip in solid ice. Changes of tidal phase and decrease in air temperature influence freezing of the strip in one-two days. While the tidal flow leaves the strait it overflows a shallow bar and generates internal lee waves propagating downslope and mixing the water. Tidal forcing of internal waves was measured using pressure gauges and by scanning of the ice surface during flood and ebb phases. Internal waves were measured using three types of CTD instruments and an ADCP current meter. The generation of wave packets occurs every tidal cycle when the current flows into the lake, but no generation occurs during the ebb phase of the tide because the currents over the bar slope are low. Parameters of internal waves are estimated. Model simulations confirm generation of internal wave train by the tidal current descending downslope.     

On the future navigability of Arctic sea routes: High-resolution projections of the Arctic Ocean and sea ice

The rapid Arctic summer sea ice reduction in the last decade has lead to debates in the maritime industries on the possibility of an increase in cargo transportation in the region. Average sailing times on the North Sea Route along the Siberian Coast have fallen from 20 days in the 1990s to 11 days in 2012–2013, attributed to easing sea ice conditions along the Siberian coast. However, the economic risk of exploiting the Arctic shipping routes is substantial. Here a detailed high-resolution projection of ocean and sea ice to the end of the 21st century forced with the RCP8.5 IPCC emission scenario is used to examine navigability of the Arctic sea routes. In summer, opening of large areas of the Arctic Ocean previously covered by pack ice to the wind and surface waves leads to Arctic pack ice cover evolving into the Marginal Ice Zone. The emerging state of the Arctic Ocean features more fragmented thinner sea ice, stronger winds, ocean currents and waves. By the mid 21st century, summer season sailing times along the route via the North Pole are estimated to be 13–17 days, which could make this route as fast as the North Sea Route.     

Influence of ice compression on components of the velocity of motion of liquid under the ice cover in a traveling periodic flexural gravity wave of finite amplitude

By the method of multiple scales, we obtain (to within the third order of smallness) the asymptotic expansions for the components of the velocity of motion of liquid under a floating ice cover in the process of propagation of periodic surface flexural gravity waves of finite amplitude under the conditions of ice compression. We study the dependences of the distributions of the velocity components along the wave profile on the compressive forces and the parameters of the initial harmonic. It is shown that the amplitude values of the velocity components decrease and the phase shift of oscillations increases as the compressiveforces increase.     

Reflected and transmitted waves in a channel with side porous mattresses

The problem of wave propagation and wave damping in a channel with side porous mattresses of arbitrary shape protruding from the walls is studied. The solution was achieved by applying 3-D boundary element method and was employed to study wave field in the channel and to analyze the effect of the geometry of the mattresses and physical and hydraulic properties of porous material on wave damping. The results show that wave damping in the channel strongly depends on wave parameters, especially, on the wave number. Wave reflection and transmission decrease with increasing the wave number. The results also show that the wave field in the channel strongly depends on the geometry of the mattresses as well as on physical and hydraulic properties of porous material used to build these wave dampers. The geometry of the mattresses and physical and hydraulic properties of porous material have a moderate effect on wave reflection and a significant effect on wave transmission. The results show that wave transmission down the channel decreases with increasing the length and thickness of the mattresses. Moreover, wave transmission decreases with increasing the porosity and damping properties of porous media used to build the mattresses. The analysis shows that porous mattresses protruding from the channel walls are very efficient in damping water waves propagating down the channel and may be built in channels to reduce high waves and achieve desired wave conditions. Theoretical results are in reasonable agreement with experimental data.     

Wave pattern induced by a moving atmospheric pressure disturbance

A moving low atmospheric pressure is a main feature of tropical cyclones, which can induce a system of forced water waves and is an important factor that cause water level rise during a storm. A numerical model based on the nonlinear shallow water equations is applied to study the forced waves caused by an atmospheric pressure disturbance moving with a constant velocity over water surface. The effects of the moving speed, the spatial scale and the central pressure drop of the pressure disturbance are discussed. The results show that the wave pattern caused by a moving low-pressure is highly related with its moving speed. The wave pattern undergoes a great change as the moving speed approaches the wave velocity in shallow water. When the moving speed is less than the wave velocity, the distribution of water surface elevation is nearly the same as that of the pressure disturbance, and the maximum of the water surface elevation is located at the center of pressure. When the moving speed is larger than the wave velocity, a triangle shaped wave pattern is formed with a depression occurs in front of the pressure center, and the maximum of the water surface elevation lags behind the center of pressure. As the moving speed increases, the maximum of the water surface elevation firstly increases and then decreases, which reaches a peak when the moving speed is close to the wave velocity. The maximum of water surface elevation is approximately in proportion to the central pressure drop, and slightly affected by the spatial scale of pressure disturbance. Both the central pressure drop and the spatial scale of the pressure disturbance do not significantly affect the forced wave pattern. However, a clear difference can be noticed on the ratio of the maximum water surface elevation in moving pressure situation to that in static situation, when the moving speed is close to the wave velocity. A pressure disturbance with smaller spatial scale and smaller central pressure drop will give a larger ratio when the moving speed is close to the wave velocity.     

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。     

Mechanism of sea ice formation based on comprehensive observation data in Liaodong Bay,China

Sea ice disaster is one of the principal natural hazards that affect some coastal areas of China,and the formation of ice cover in a wave field has important characteristics.However,analysis of the mechanism in which waves affect the thermodynamic process of sea ice is lacking,and the influence of waves is not taken into consideration in numerical models of sea ice,largely because of a lack of simultaneous observations of waves and sea ice.Using observational data of the sea ice cycle in the coastal waters of Liaodong Bay(China),we analyzed the characteristics of hydrology,meteorology,and sea ice thickness during the formation of sea ice,and explored the changes in the interrelationships among heat fluxes,waves,and sea ice under actual sea conditions.The results could provide a decision-making support as a reference to the establishment and improvement of China's early waming system to sea ice disasters,and the protection of ice drilling operations and production platform safety.     

Body motion in liquid under ice plate with snow cover

The motion of a submarine in liquid under an ice plate covered with flooded snow is considered. The ice is modelled as an elastic plate and the snow cover is modelled as a viscous layer on the top of the plate. The submarine is modelled as a slender solid of revolution with scale 1:300. The experimental and theoretical study of the influence of the viscous snow layer on deflections of the floating ice plate is conducted. The viscous layer reduces the amplitudes of flexural-gravity waves. The greatest influence of the viscous layer on the plate deflections is achieved for velocities of the submarine, where the waves of maximum amplitude are generated. Theoretical results are in good qualitative and quantitative agreement with the model experiments.     

Automatic Profiling System for Underice Measurements

The article is devoted to the development of an autonomous profiling system for measuring the aquatic environment under ice. The system moves up and down in the water column along a cable with a load at the lower end, which is lowered into a lane in the ice. The system carrier is designed for transporting an acoustic Doppler current profiler and a salinity, temperature, and pressure probe. The system will be useful for long-term measurements of vertical profiles of the current speed and marine environment parameters, as well as ice draft. The article describes in detail the structure and operation of the system. The hydraulic scheme of the carrier buoyancy system is presented.

     

Incidence of flexural gravitational waves on the line of contact of two floating ice plates of different thickness

We analyze the influence of a rift in an ice field on the propagation of flexural gravitational waves in a basin of finite constant depth. The ice cover is simulated by two floating semiinfinite elastic plates of different thickness. We studied the dependence of the amplitude coefficients of reflection and transmission of waves incident on the rift on the frequency of running waves, the thickness of ice on both sides of the rift, and the type of contact boundary conditions at the rift. Translated by Peter V. Malyshev and Dmitry, V. Malyshev     

Edge waves under ice cover at a straight coast with a sloping beach

Edge waves in an ice-covered sea at a straight coast with a sloping beach are analyzed within the linearized theory. Such waves propagate along the coast with an amplitude which exponentially decays offshore. The problem is examined without using the hydrostatic assumption. The seawater is considered to be a homogeneous, inviscid, nonrotating, and incompressible fluid. Ice with a uniform thickness is considered, with constant values of density, cylindrical rigidity, Poisson ratio, and compressive stress in the ice. The normal velocity at the bottom is zero; the linearized kinematic and dynamic boundary conditions are satisfied at the lower surface of the ice. Explicit solutions for the edge flexural-gravity waves and the corresponding dispersion equations are obtained and analyzed.