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.     

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.     

Wave power extraction from an oscillating water column along a straight coast

In order to study the effects of coastline on wave power absorption, we describe here a linearized theory of an oscillating water column (OWC) installed on a straight coast. The sea depth is assumed to be constant and the coast is a vertical cliff. The column is a vertical circular cylinder half embedded in the cliff and open on the seaside. Forced by incident waves from any direction, the water surface inside pushes the dry air above through a Wells turbine system to generate power. Carrying out the linearized theories of radiation and diffraction analytically, we calculate the coefficients of apparent mass and radiation damping, and the chamber pressure. Optimum absorption efficiency is examined under the constraint of constant chamber volume. Results are compared with a parallel study of an OWC installed either offshore or at the tip of a thin breakwater.     

Three-dimensional experiments on landslide generated waves at a sloping coast

This paper describes new three dimensional experiments on water waves generated by landslides. The landslide is reproduced by a rigid elliptical body, sliding along an inclined plane (slope of 1/3, 1 vertical, 3 horizontal). The generated water waves are free to propagate both offshore and alongshore, since the plan dimensions of the used wave tank are of at least one order of magnitude larger than the width of the landslide, which can be considered to be a scale of the wave length. The experimental study has been carried out reproducing both subaerial and partially submerged landslides. The wave generation process is studied by means of video records of the near field flow and measurement of the landslide movement; the properties of the waves propagating along the coast are described on the basis of runup gauges. The waves observed during the experiments always present first a crest and then a trough; as the first wave propagates away from the generation area the crest tends to become smaller than the trough and the maximum runup along the coast is given by the second or by the third wave. An important feature is that the observed runup along the coast firstly grows with the distance from the generation area, it reaches a maximum value at about two times the width of the landslide, and then decreases. An estimate of the celerity at which the waves propagate along the coast is given on the basis of gauge measurements; it results that the crests propagate faster than the troughs, and the wave period increases.     

The role of bottom friction in models of nonbreaking tsunami wave runup on the shore

The role of bottom friction in the runup of nonbreaking long waves on the shore is analyzed. The case of the normal incidence of monochromatic waves is considered. The relief of the model region consists of an even horizontal bottom area conjugated with a flat slope. The energy dissipation is estimated as the work of bottom friction forces over the wave field obtained using the known analytical solution based on the Carrier-Greenspan transforms. Estimates of energy losses for waves whose periods are typical for tsunami waves have been obtained. The energy dissipation is shown to be not concentrated in the shore line area as a rule. The question about the practicability of using partially reflecting boundary conditions on the coast to take into account the bottom friction in large-scale models of tsunami propagation is considered.     

Large-time response of ice cover to a load moving along a frozen channel

Unsteady response of an ice cover in a channel with vertical walls is studied for large times. The ice deflection is caused by a load moving along the frozen channel at a constant speed. The ice cover is modelled as a thin elastic plate clamped to the walls of the channel. The time-dependent problem is solved by using the Fourier transform along the channel and the method of separating variables. In the system moving along the channel together with the load, the large-time deflection of the ice cover consists of steady deflection and standing waves in front and behind the load. The number of waves, their frequencies and wavenumbers depend on the speed of the load and the values of the critical speeds for the channel. The number of the waves and their amplitudes are calculated for a given load and its speed. The maximum stress in the ice as a function of the load speed is estimated.     

Numerical modeling of the propagation and strengthening of tsunami waves near the Crimean Peninsula and the Northeast Coast of the Black Sea

The linear model of long waves is used for the evaluation of the parameters of tsunami waves along the South Coast of Crimea, in the near-Kerch zone, and near the northeast coast of the Black Sea. Our numerical investigations are carried out for 24 probable locations of the elliptic zones of tsunami generation over the continental slope of the basin. The amplitude characteristics of tsunamis are computed for 27 sites of the Black-Sea coast. It is shown that significant strengthening of tsunami waves is possible in the course of their propagation toward the coast. The highest waves are formed at the sites of the coast closest to the seismic source. The dependence of the intensity of tsunami waves along the Black-Sea coast on the location of the seismic source and its magnitude is analyzed.     

Coastline sand waves on a low-energy beach at “El Puntal” spit, Spain

Coastline sand waves have been observed at “El Puntal” spit, located on the north coast of Spain. The spit has been monitored by an Argus video system since 2003 and the formation and destruction of sand waves has been observed. Coastline data from the video images are analyzed by means of principal components analysis, obtaining a mean sand wave length of 125–150 m and a maximum amplitude of ≈ 15 m. It is also observed that sand waves reach their maximum amplitude at about 15 days. No propagation of these sand waves is noticed during the approximately two-month-long events analyzed. Sand wave formation and evolution are examined in relation with the prevailing local wave conditions during that period. Incident waves at the west end of the spit approach from the east–northeast, with a very high angle with respect to the shoreline. Field observations suggest that sand waves may result from an instability in alongshore sediment transport caused by moderate-energy waves with a high-angle incidence.     

Wave diffraction of breakwaters in the presence of a coastline

An integral method is described which is capable of computing the diffraction field produced by waves incident on a breakwater connected to or placed near a straight coastline. Some simple configurations are studied: a straight breakwater protruding normally from the coast, a straight breakwater parallel to the coast, an ‘elbow-shaped’ breakwater with one end connected to the coast, a pair of straight breakwaters protruding normally from the coast and a series of three equal straight breakwaters parallel to the coast. In all cases the water depth is assumed to be constant, while both the breakwater and the coastline walls are supposed to be perfectly reflective. Within the limits of these hypotheses the method is rather general, because breakwaters of arbitrary shape can be considered.     

近岸波浪和波生流环境中泥沙输运的数值模拟

Owing to lack of observational data and accurate definition,it is difficult to distinguish the Kuroshio intrusion water from the Pacific Ocean into the South China Sea(SCS).By using a passive tracer to identify the Kuroshio water based on an observation-validated three-dimensional numerical model MITgcm,the spatio-temporal variation of the Kuroshio intrusion water into the SCS has been investigated.Our result shows the Kuroshio intrusion is of distinct seasonal variation in both horizontal and vertical directions.In winter,the intruding Kuroshio water reaches the farthest,almost occupying the area from 18°N to 23°N and 114°E to 121°E,with a small branch flowing towards the Taiwan Strait.The intrusion region of the Kuroshio water decreases with depth gradually.However,in summer,the Kuroshio water is confined to the east of 118°E without any branch reaching the Taiwan Strait;meanwhile the intrusion region of the Kuroshio water increases from the surface to the depth about 205 m,then it decreases with depth.The estimated annual mean of Kuroshio Intrusion Transport(KIT) via the Luzon Strait is westward to the SCS in an amount of –3.86×106 m3/s,which is larger than the annual mean of Luzon Strait Transport(LST) of –3.15×106 m3/s.The KIT above 250 m accounts for 60%–80% of the LST throughout the entire water column.By analyzing interannual variation of the Kuroshio intrusion from the year 2003 to 2012,we find that the Kuroshio branch flowing into the Taiwan Strait is the weaker in winter of La Ni?a years than those in El Ni?o and normal years,which may be attributed to the wind stress curl off the southeast China then.Furthermore,the KIT correlates the Ni?o 3.4 index from 2003 to 2012 with a correlation coefficient of 0.41,which is lower than that of the LST with the Ni?o 3.4 index,i.e.,0.78.     

The influence of snow viscosity on forced flexuralgravity waves in a basin with a density jump

The effect of the internal friction of snow covering floating ice on small-amplitude waves generated by a periodic-in-time source in a basin with a density jump is considered. The dependences of amplitude-phase characteristics of the wave disturbances induced by surface and internal waves on the snow viscosity coefficient, the oscillation frequency, and the depth of the source are studied.Translated by V. Puchkin.     

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.     

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.     

Run-Up of a Solitary Tsunami Wave on a Sloping Coast

Within the framework of the nonlinear theory of long waves, we perform the numerical analysis of the one-dimensional run-up of solitary tsunami waves upon a plane sloping coast. We study the dependences of the run-up heights on the parameters of waves at the entrance of the shelf zone and on the slope of the coast. The run-up heights of tsunami waves are estimated for the bottom topography typical of the south coast of the Crimean Peninsula. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 11–18, July–August, 2005.     

The attenuation of bending-gravity waves

The influence of the internal friction of snow covering solid elastic floating ice on the waves in a basin with density shear is considered. Dispersion dependences and spatial-temporal attenuation of surface and internal waves are investigated. The role of snow in the formation of the structure of ice bending deformations and fluid disturbances is determined.Translated by Mikhail M. Trufanov.     

Topographically trapped waves over the continental shelf and slope

General characteristics of topographically trapped subinertia waves are discussed from the viewpoint of an eigenvalue problem and ray theory. Special attention is paid to the slope parameterS(x) (=(dh/dx)/h, wherex denotes the coordinate perpendicular to the shoreline, increasing seaward, andh(x) is the depth) which is a measure of the strength of the restoring force of the waves. Three cases for theS distribution are considered, in whichS is assumed to be positive at the coast and to tend to zero far from the coast. The first is whereS(x) decreases monotonically towards the open ocean. It is found in this case that waves are trapped near the coast. The second is whereS(x) does not decrease monotonically, but has a maximum. It is concluded that this case may contain two types of waves, i.e., those trapped near the coast and those trapped near the maximum, and the dispersion curves corresponding to different types may nearly intersect, namely, result in “kissing”. The third is whereS(x) has a negative region (corresponding to the presence of a trench). It is found in this case that an infinite sequence of waves is trapped in the negativeS region which propagate with the coast to their left (right) in the northern (southern) hemisphere besides the waves trapped near the coast. The topography in the second case corresponds to a typical continental shelf and a typical continental slope. It is shown by model calculation that trapped waves are present over the continental slope as well as over the continental shelf. Almost the same results are obtained for superinertia waves ifS is replaced by 1/h which is a measure of the restoring force of superinertia waves.     

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.     

Short-period internal waves in an arctic Fjord (Spitsbergen)

Measurements of temperature and salinity in the frequency range of short-period internal waves are considered. The measurements were carried out in the Van Mijen Fjord in Spitsbergen. The dominating periods of short-period internal waves are equal to a few minutes. They correspond to an internal wave with a dimensionless wavenumber 1/2. The generation of short-period internal waves is determined by external forcing from wind and tide. In winter, when the surface of the fjord is covered with ice, the wind stress is not transferred to the internal oscillations and the spectral level of internal waves decreases.     

Onset of coastal upwelling in a two-layer ocean by wind stress with longshore variation

On the assumption that motions of the barotropic mode are horizontally nondivergent, action of the wind stress with longshore variation on a two-layer ocean adjacent to the meridional east coast is studied. Only the equatorward wind stress is considered. Along the east coast, upwelling is induced by the direct effect of the coast and is confined in a narrow strip with the width of the order of the internal radius of deformation. The upwelling propagates poleward with the internal gravity wave speed. Coastal upwelling induced by the wind stress with longshore variation may be interpreted as the generation and propagation of internal Kelvin waves. Associated with the coastal upwelling, the equatorward flow in the upper layer and the poleward flow in the lower layer are formed as an internal mode of motions. When the bottom topography with the continental shelf and slope is taken into account, occurrence of the poleward undercurrent is delayed by a few days because of the generation of continental shelf waves. And, after the forcing is stopped, the shelf waves propagate poleward away from the upwelling region and the poleward undercurrent fully develops. At the margin of the continental shelf, another upwelling region is induced and propagates poleward.     

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.