Ice Pile Research Articles

The range of ice thrusts and ice piles as reflected by ice scars on trees growing on the shores of coastal lagoons: The case of the Szczecin Lagoon

We studied the phenomena associated with the thrusting of ice onto the shore of the Szczecin Lagoon based on the occurrence of tree ice scars. The measurements concerned mostly the maximum height, length and width of ice scars on trees, and the distance of these trees from the shore in the period 2017–2022. It was observed that sheets of ice advanced up to 64 m inland, and piled to form hummocks reaching up to 4.3 m above the water level. These maximum values occurred mostly on eastern shores, which is where the highest numbers of damaged and broken trees were observed. This should be associated with the strongest and most frequently occurring wind blowing from the western direction in the winter-spring period. To the contrary, the lowest number of damaged trees were observed on the western shore. This is due not only to the lower frequency of wind blowing from the east, and the associated cooling (Ta < 0°C) and ice cover stabilization, but also due to the presence of extensive reed belts. Our results enable an indirect insight into the ice phenomena dynamics, especially in areas lacking systematic ice observations. Similar conclusions may be extended for all the sheltered basins as lakes or lagoons.

Wind Drift, Breakdown, and Pile Up of the Ice Field

This article contains the analytical model of the drift of a separate ice field under the action of wind and current, in which velocities and directions can vary over time. The model takes into account the mass of ice, added mass of seawater, and the effects of the wind and current on the ice field in forming the friction on its upper and underwater surfaces and the frontal resistance on its end (forward and backward) surfaces. Simulation of the wind drift of the ice field showed the drift velocity exceeds the considerable known velocity of a compact ice cover drift. A drifting ice field has a certain kinetic energy that should be released when a collision occurs with an unmovable obstacle, and spent on brittle breakdown of a quantity of the ice field. The volume of formed small ice pieces (fragments of ice field) was estimated by comparison of the specific energy of the sea ice brittle destruction and the kinetic energy of the drifting ice field. The article presents the results of the estimation of the possible volume of the ice pieces and the scales of formed piles as a result of a collision with an obstacle, depending on the initial dimensions of the ice field and wind speed. Developed models and the results of computer modeling can be used to estimate the ice pile sizes near the stationary platforms and terminals on the Arctic seas.

Ice interaction processes during ice encroachment

Ice encroachment is the accumulation of ice atop a platform and results when ice drifts against a platform. Most often this occurs in shallow water but in principle can occur in deep water if the ice drift length is long enough. As the ice drifts against the platform it is broken and generates rubble and ice piles in front of the platform, and with sufficient drift duration blocks of ice can be pushed up and onto the platform. This must be taken into account when designing structures in the Caspian Sea and other shallow water areas where there is significant ice drift. Ice can encroach on the structure by ice ride-up and pile-up. Consequently, the height and extent of the ice piling up on top of the structures must be taken into account in designing the layout, and often a protective ice encroachment zone is made all around the structure. The aim of this paper is to provide an outline of various approaches and parameters to consider where ice encroachment may occur. The study is supported by analysis of dedicated ice model test data, numerical simulations using Discrete Element Models, and full scale data of ice encroachment events. The intent is to give an understanding of the physics of ice encroachment and support in the design of shallow water offshore structures. In particular, the results indicate the importance of ice strength in the process and especially the maximum pile height. If the ice is weaker, the pile grows horizontally in a seaward direction in front of the structure, and conversely, stronger ice forms ice encroachment with greater vertical and also horizontal extent on the platform. The results also show that once the maximum pile height is established subsequent drift enlarges the seaward extent of the rubble pile in front of the structure.

Classification criterion of narrow/wide ice-resistant conical structures based on direct measurements

Ice-induced structural vibration generally decreases with an increase in structural width at the waterline. Definitions of wide/narrow ice-resistant conical structures, according to ice-induced vibration, are directly related to structure width, sea ice parameters, and clearing modes of broken ice. This paper proposes three clearing modes for broken ice against conical structures: complete clearing, temporary ice pile up, and ice pile up. In this paper, sea ice clearing modes and the formation requirements of dynamic ice force are analyzed to explore criteria determining wide/narrow ice-resistant conical structures. According to the direct measurement data of typical prototype structures, primary quantitative criterion of the ratio of a cone width at waterline (D) to sea ice thickness (h) is proposed. If the ratio is less than 30 (narrow conical structure), broken ice is completely cleared and a dynamic ice force is produced; however, if the ratio is larger than 50 (wide conical structure), the front stacking of broken ice or dynamic ice force will not occur.

An efficient algorithm for generating symmetric ice piles

We define the Symmetric Ice Pile ModelSIPMk(n), a generalization of the Ice Pile ModelIPMk(n), and we show an efficient algorithm for generating the symmetric ice piles with n grains. More precisely, we show how to exploit an existing algorithm for generating IPMk(n) in order to generate SIPMk(n) in amortized time O(1) and in space O(kn).

A recursive structure of sand pile model and its applications

Abstract The Sand Pile Model (SPM) and its generalization, the Ice Pile Model (IPM), originate from physics and have various applications in the description of the evolution of granular systems. In this article, we deal with the enumeration and the exhaustive generation of the accessible configuration of the system. Our work is based on a new recursive decomposition theorem for SPM configurations using the notion of staircase bases. Based on this theorem, we provide a recursive formula for the enumeration of SPM(n) and a constant amortized time (CAT) algorithm for the generation of all SPM(n) configurations. The extension of the same approach to the Ice Pile Model is also discussed.

Forms of Onshore Ice Thrusting in Coastal Lagoons of the Southern Baltic Sea

AbstractHydrometeorological conditions of ice field onshore thrusting and its forms were explored in the Szczecin and Vistula lagoons. Five well-documented cases of ice sheet thrusting to more than 100 m inland are presented. Four cases (March 1, 1976; January 14, 1993; January 28, 2003; and February 1, 2004) were observed in the Szczecin Lagoon, one (February 8, 2011) occurring in the Vistula Lagoon. In both areas, the ice field onshore thrusting was driven mainly by strong winds following a cold front in a deep baric low. The longest thrusts, several to 150-m wide, pushed the ice sheet 140 m inland. Near the shore, the sheets were alternated by ice hummocks. The ice sheet base was usually flanked by elongated, low ice piles. The ice sheet tapered inland, its edges rounding off. The thrust ice sheets were finger, tongue, half-ellipse, or semicircle shaped, and they were distinctly rounded in the frontal part.

Experiments on level ice loading on an icebreaking tanker with different ice drift angles

Abstract A series of tests was performed with a laboratory-scale model ship to simulate the effects of ice load parameters on an icebreaking tanker. A model of the icebreaking tanker Uikku was mounted on a rigid carriage and towed through an unbroken ice sheet in the ice tank of the Marine Technology Group at Aalto University. Two ice sheets and 11 different experimental configurations were used. The carriage speed, heading angle of the model ship, and ice thickness were varied, and the forces, accelerations, ice cusp sizes, carriage positions, and ice pile dimensions under the intact ice sheets were measured. This paper includes results for the measurements of ice rubble loads against the model hull in the horizontal plane. Phenomena such as ice failure modes and ice rubble accumulation on the upstream side of the hull beneath the ice sheet were observed in some tests. The icebreaking lengths and dimensions of ice rubble were analyzed for some tests. The effects of towing speed, heading angle under the intact ice sheet in front of the hull, and the accompanying ice loads on the formation and build-up of ice rubble were analyzed. In addition, the evolution of ice rubble geometry, in cross sections and the horizontal plane, was investigated. There was good agreement over several orders of magnitude between the measured and calculated values of the lateral ice forces. These results are relevant to the modeling of ice loading on hulls and the design of moored or dynamic positioned structures for operation in ice-covered waters. Some parameters obtained from these tests can be used as input for future numerical simulations.

A CAT algorithm for the exhaustive generation of ice piles

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model (n), a generalization of the sand pile model (n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice (n): this lets us design an algorithm which generates all the ice piles of (n) in amortized time O(1) and in space O( ).

A method of calculating ice loads when ice piles up on a fixed wall

A model for calculating ice loads on a shelf ice-resistant platform is developed which corresponds to a cyclic scenario of the interaction of ice with the wall of a platform observed in laboratory experiments. Using relations which follow from the laws of conservation of mass, momentum and energy written for ice which fills a ridge formed at the wall of the platform, an explicit formula is obtained for the ice load on the wall. The generalized forces characterizing the dependence of the energy dissipation accompanying ridging on the dimensions of the sail and keel of the ridge and on the shape of the wall are parametrized. It is shown that the calculated loads obtained using the assumption of hydrostatic equilibrium of the sail and the keel of the ridge correspond to the lower boundary of the experimentally measured loads. The calculated loads obtained using the assumption that the keel of a ridge is of constant size yield an upper estimate of the ice loads. In order to estimate the limit loads at which collapse of the ice into the water occurs, a problem on the formation of a flexural crack in an ice floe which is thrust onto the wall is considered. The average and maximum ice loads on the wall of a platform are calculated on a real scale.

Ice conditions in coastal lakes of the southern Baltic Sea

This paper describes spatio-temporal variability of the basic ice condition parameters, relationships between selected lakes in terms of those parameters, and frequency of fast (ice cover) and floating ice. Attention is also paid to morphology and topography of ice cover in lakes Jamno, Bukowo, Gardno, and Lebsko during 1960/61-1999/2000. Based on data archived at the Institute of Meteorology and Water Management, the following ice parameters were analysed: date of the first ice appearance; date of the first ice cover formation, date of disintegration of the last ice cover, date of disappearance of the last ice, ice season duration, number of days with ice, number of days with ice cover, ice conditions continuity, and maximum ice thickness in winter. Lakes Jamno and Bukowo, located in the western part of the Polish coast, are characterised by milder ice conditions, compared to the more eastward lakes (the Gardno and the Lebsko). Ice parameters were found to correlate closely, with statistical significance exceeding a = 0.01 and correlation coefficients usually higher than 0.90, between individual lakes, particularly the neighbouring ones. The highest frequencies of fast and floating ice, 70-75 % and about 10 %, respectively (altogether more than 80 %), were recorded in the last pentade of January. Fast ice (ice cover), accounting for 80 % of all the ice types, was found to dominate in the lakes studied; fast ice domination is typical of small and shallow water bodies. Ice cover is formed as a result of uniform increase in ice rind thickness. After the fast ice has decayed, an ice field pushed by the wind may form ice piles rising to a few metres above the water surface. At the beginning of the ice season, the piled ice appears most often on the western and northern shores, while at the end of the season it tends to stay on the eastern shores. The processes, associated with the presence of piled ice on the shore, are destructive not only for the shore, but also for constructions deployed within the ice range. The ice piles also affect transport and accumulation of sediment, mainly in the shore zone.

Enumeration of sand piles

We study some particular families of integer partitions called “sand piles” which are discrete dynamical systems. Our aim is to link these objects with the theory of partitions in order to enumerate them. We first consider the Ice Pile model IPM( k). We compute explicit asymptotic bounds for the number of sand piles in IPM( k) with area n. We then give the area, width and height generating functions. All these results are derived using bijections and q-equations. We then consider another model called L( θ).

Games on line graphs and sand piles

The dynamics of several games on line graphs is studied. Relations between these games and a one-dimensional version of the sand pile model are established. We also study a generalization of the latter model, which we call the ice pile model. Specifically, we investigate the dynamical behavior of all these games and provide closed formulas for the transient time lengths they require to reach the steady state.

Laboratory‐scale simulation of under‐ice reflectivity at low frequencies

Under‐ice reflectivity is dominated by sea ice ridges, long, randomly spaced, randomly oriented rubble piles of broken ice. The effective low‐frequency shear and compressional velocities of these formuations have been estimated to be between 1100–1700 and 2700–3400 m/s, respectively (Diachok, Proceedings International Congress on Acoustics, 1986). To be consistent with these estimates, Lucite, a readily available and easily machined material, for which Vs = 1260 m/s and Vp = 2600 m/s was used to construct laboratory scale analogs of sea ice ridges situated on a thin plate. Both parallel and randomly oriented ridge models were construtted, and the effects of ridge elasticity and orientation on under‐ice reflectivity (amplitude and phase) were examined for 0.67 < ka < 6 (k = wavenumber and a = mean depth). Initial reflection coefficient data at the lowest frequencies are approximately consistent with Twersky's predictions for reflectivity from both hard and soft half‐cylinders on a soft boundary. Higher fre...

A Wind-Driven Ice-Push Event in Eastern Lake Ontario

Ice on Lake Ontario at Kingston weakened rapidly in warm air temperatures to 17° C on the afternoon of 26 March 1986. Moderate onshore winds to 33 km/h changed to offshore winds during the night, and by morning most of the ice in the nearshore area had blown’more than 5 km offshore. After 0600 on the morning of 28 March winds shifted to an obliquely onshore direction, increasing to 28 km/h by noon and driving the ice onshore. A small ice-push event occurred at 1225 lasting 10 minutes, piling ice to a height of 2.5 m above the bank by successive overriding. Eleven stones of up to 206 kg were moved from the shore by the body of the ice and carried up, in some cases, to near the top of the ice pile, despite the weakness of the thin, candled ice sheet. The need for quantitative studies of these irregular and unpredictable events is demonstrated by these observations.

Possible effects of snow layer absorption on under ice reflectivity

Sea ice, which consists of relatively flat plates (nominally 2.5‐m thick), randomly interrupted by ridges (rubble piles of broken ice), is generally coverged by a thin layer (nominally 0.2 m) of snow. The reflection coefficient from snow‐covered sea ice plates, computed with the FFP, reveals generally large losses at frequencies higher than 100 Hz and grazing angles greater than 10°. Losses are maximum for frequency‐angle combinations that permit conversion to Lamb modes in the ice plate. Loss magnitudes are particularly sensitive to the snow layer absorption coefficient. Computed results are consistent with reflectivity versus frequency and grazing angle (Θ > 14.3°) measurements reported by Yang and Votaw [J. Acoust. Soc. Am. (1981)], assuming their estimates of plate thickness and historical ice and snow velocity, density, and absorptivity data. At grazing angles less than 10° computations suggest that snow effects on the reflection coefficient are small, a result which is consistent with the hypothesis that long‐range under‐ice propagation loss is dominated by ridges [Diachok, J. Acoust. Soc. Am. (1976).]

The Occurrence of Grounded Ice Ridges and Shore Ice Piling along the Northern Coast of Somerset Island, N.W.T.

Massive shore ice piles and grounded ice ridges up to 30 m high were examined along the northern coast of Somerset Island between 1973 and 1976. The ice ridges, composed of 1 to 2 m thick ice blocks and occasionally thicker multi-year ice blocks, occurred most frequently along the north and west shores of capes and headlands. 'Cape Fisher' was the site of shore ice piling during each of the four years and one set of ice piles, built 15-60 m inland existed three years. Effects of grounded ice ridges on nearshore morphology were minimal but ice-push features were observed as much as 185 m inland across the beach.

Contributions to the Glacial Geology of Spitsbergen

On June 17th, 1896, the tercentenary of the discovery of Spitsbergen by Barentz, we first sighted the western coast of the great island, the unknown interior of which Sir Martin Conway's expedition had been organized to explore. The sea was strewn with floes, which barred direct approach to the shore, and the incidents of the passage through the ice helped us to realize that we were 13° north of the Arctic Circle, far within the area which, according to a once popular theory, was formerly buried beneath a massive cap of ice. But the first near view of the land was calculated to destroy whatever faith we might have had in the former existence of a north polar ice-cap. For the sharp, serrated ridges of Mount Starashchin (see Pl. XIX, fig. 2) and Dodman Den, which guard the entrance to Ice Fiord, indicate that Western Spitsbergen has not at any recent time been wholly submerged beneath an ice-cap. Confluent series of glaciers occur in Spitsbergen at the present day, and form the so-called ‘inland ice-sheets.’ One such can be seen to the north of Ice Fiord, rising gradually from the shore to the sky-line; while on the plateau south of the fiord are smaller, disconnected glaciers. Hence, during the passage up Ice Fiord, between the great ice-sheet to the north and the scattered glaciers to the south, through the ice-floes among which the steamer carefully threaded its way, and past the huge piles of ice heaped along the shore, we