Floe Diameter Research Articles

Ship resistance when operating in floating ice floes: Derivation, validation, and application of an empirical equation

With the effects of global warming, the Arctic is presenting a new environment where numerous ice floes are floating on the open sea surface. Whilst this has improved Arctic shipping navigability in an unprecedented way, the interaction of such floes with ships is yet to be understood to aid the designing of ships and route planning for this region. To further explore this topic, the present work develops a procedure to derive an empirical equation that can predict the effects of such floes on ship resistance. Based on a validated computational approach, extensive data are extracted from simulations of three different ships with varying operational and environmental conditions. The ice-floe resistance is shown to strongly correlate with ship beam, ship buttock angle, ship waterline angle, ship speed, ice concentration, ice thickness and floe diameter, and the regression powers of each of the parameters on resistance are ascertained. This leads to a generic empirical equation that can swiftly predict ice-floe resistance for a given ship in a given condition. Subsequently, demonstrations are given on the incorporation of the derived equation into a set of real-time Arctic ship performance model and voyage planning tool, which can predict a ship's fuel consumption in ice-infested seas and dynamically suggest a route with the least safety concern and fuel consumption. Moreover, the equation is validated by providing ice resistance prediction for experimental and full-scale conditions from multiple sources, showing high accuracy. In conclusion, the empirical equation is shown to give valid and rapid estimates for ice-floe resistance, providing valuable insights into ship designs for the region, as well as facilitating practical applications for polar navigation.

A Computational Fluid Dynamics Model for the Small-Scale Dynamics of Wave, Ice Floe and Interstitial Grease Ice Interaction

The marginal ice zone is a highly dynamical region where sea ice and ocean waves interact. Large-scale sea ice models only compute domain-averaged responses. As the majority of the marginal ice zone consists of mobile ice floes surrounded by grease ice, finer-scale modelling is needed to resolve variations of its mechanical properties, wave-induced pressure gradients and drag forces acting on the ice floes. A novel computational fluid dynamics approach is presented that considers the heterogeneous sea ice material composition and accounts for the wave-ice interaction dynamics. Results show, after comparing three realistic sea ice layouts with similar concentration and floe diameter, that the discrepancy between the domain-averaged temporal stress and strain rate evolutions increases for decreasing wave period. Furthermore, strain rate and viscosity are mostly affected by the variability of ice floe shape and diameter.

Ship resistance when operating in floating ice floes: A combined CFD&DEM approach

Whilst climate change is transforming the Arctic into a navigable ocean where small ice floes are floating on the sea surface, the effect of such ice conditions on ship performance has yet to be understood. The present work combines a set of numerical methods to simulate the ship-wave-ice interaction in such ice conditions. Particularly, Computational Fluid Dynamics is applied to provide fluid solutions for the floes and it is incorporated with the Discrete Element Method to govern ice motions and account for ship-ice/ice-ice collisions, by which, the proposed approach innovatively includes ship-generated waves in the interaction. In addition, this work provides two algorithms that can implement computational models with natural ice-floe fields, which takes floe size distribution and randomness into consideration thus achieving high-fidelity modelling of the problem. Following validation against experiments, the model is shown accurate in predicting the ice-floe resistance of a ship, and then a series of simulations are performed to investigate how the resistance is influenced by ship speed, ice concentration, ice thickness and floe diameter. This paper presents a useful approach that can provide power estimates for Arctic shipping and has the potential to facilitate other polar engineering purposes.

Investigation of two pack ice besetting events on the Umiak I and development of a probabilistic prediction model

Pack ice besetting events are defined as incidents in which a typical ice-class vessel encounters dynamic sea ice conditions which are beyond the ship's icebreaking and maneuverability capacities, and the vessel becomes stuck in the pack ice until such conditions subside. Besetting events can cause severe disruption to a vessel's transit schedule, leading to increased operational downtime, and ship crew and fuel costs. Hence, predicting the probability of occurrence of these events can help vessel operators plan in advance accordingly, possibly rerouting the vessel, and saving operational costs. In this paper, two pack ice besetting events experienced by the Umiak I, an icebreaking bulk carrier owned and operated by Fednav Limited which runs nickel ore from the mine at Voisey's Bay, Labrador to Québec City, are analyzed in terms of the wind, surface ocean current, and sea ice conditions which caused them. The particular metocean and pack ice conditions associated with the occurrence of these events are used to develop a framework for a model to predict the future occurrence of such events for the Umiak I and quantify probabilities of besetting event occurrence linked to specific sets of coincident metocean and ice conditions. The model will serve as a tool for predicting besetting event probabilities during Umiak I navigations, as well as in hindcast shipping feasibility studies, to determine the likelihood of besetting for vessels with Umiak I capabilities in regions of new operations. The factors considered in this study are the vessel distance to the nearest coastline, regional wind and surface current speed, direction relative to the nearest coastline, divergence, and vorticity. The ice factors considered are the total concentration, mean thickness, and floe size (this represents a mean floe diameter). The datasets analyzed in this paper suggest the primary causes of the two besetting events experienced by the Umiak I in 2012 and 2013 were the relatively large ice floes encountered by the vessel (the majority of the floes during the besetting events were greater than 6 km in diameter), in combination with a convergent regional wind field and onshore winds and currents.

Quantifying Growth of Pancake Sea Ice Floes Using Images From Drifting Buoys

AbstractNew sea ice in the polar regions often begins as small pancake floes in autumn and winter that grow laterally and weld together into larger floes. However, conditions in polar oceans during freezeup are harsh, rendering in situ observations of small‐scale sea ice growth processes difficult and infrequent. Here we apply image processing techniques to images obtained by drifting wave buoys (SWIFTs) deployed in the autumn Arctic Ocean to quantify these processes in situ for the first time. Small pancake ice floes were observed to form and grow gradually in freezing, low‐wave conditions. We find that pancake floe diameters are limited by the wave field, such that floe diameter is proportional to wavelength and amplitude over time. Floe welding correlates well with sea ice concentration, and the observations can be used to estimate a key model parameter for floe size evolution. There is some agreement between observed lateral growth rates and those predicted using a theoretical model based on heat flux balance, but the model lateral growth rates are too conservative in these conditions. These results will be used to inform description of lateral floe growth and floe welding in new models that evolve sea ice floe size distribution.

Consistent biases in Antarctic sea ice concentration simulated by climate models

Abstract. The simulation of Antarctic sea ice in global climate models often does not agree with observations. In this study, we examine the compactness of sea ice, as well as the regional distribution of sea ice concentration, in climate models from the latest Coupled Model Intercomparison Project (CMIP5) and in satellite observations. We find substantial differences in concentration values between different sets of satellite observations, particularly at high concentrations, requiring careful treatment when comparing to models. As a fraction of total sea ice extent, models simulate too much loose, low-concentration sea ice cover throughout the year, and too little compact, high-concentration cover in the summer. In spite of the differences in physics between models, these tendencies are broadly consistent across the population of 40 CMIP5 simulations, a result not previously highlighted. Separating models with and without an explicit lateral melt term, we find that inclusion of lateral melt may account for overestimation of low-concentration cover. Targeted model experiments with a coupled ocean–sea ice model show that choice of constant floe diameter in the lateral melt scheme can also impact representation of loose ice. This suggests that current sea ice thermodynamics contribute to the inadequate simulation of the low-concentration regime in many models.

Surge motion of an ice floe in waves: comparison of a theoretical and an experimental model

AbstractA theoretical model and an experimental model of surge motions of an ice floe due to regular waves are presented. The theoretical model is a modified version of Morrison’s equation, valid for small floating bodies. The experimental model is implemented in a wave basin at a scale 1:100, using a thin plastic disc to model the floe. The processed experimental data display a regime change in surge amplitude when the incident wavelength is approximately twice the floe diameter. It is shown that the theoretical model is accurate in the high-wavelength regime, but highly inaccurate in the low-wavelength regime.

The seasonal evolution of sea ice floe size distribution

AbstractThe Arctic sea ice cover undergoes large changes over an annual cycle. In winter and spring, the ice cover consists of large, snow‐covered plate‐like ice floes, with very little open water. By the end of summer, the snow cover is gone and the large floes have broken into a complex mosaic of smaller, rounded floes surrounded by a lace of open water. This evolution strongly affects the distribution and fate of the solar radiation deposited in the ice‐ocean system and consequently the heat budget of the ice cover. In particular, increased floe perimeter can result in enhanced lateral melting. We attempt to quantify the floe evolution process through the concept of a floe size distribution that is modified by lateral melting and floe breaking. A time series of aerial photographic surveys made during the SHEBA field experiment is analyzed to determine evolution of the floe size distribution from spring through summer. Based on earlier studies, we assume the floe size cumulative distribution could be represented by a power law D−α, where D is the floe diameter. The exponent α as well as the number density of floes Ntot are estimated from measurements of total ice area and perimeter. As summer progressed, there was an increase in α as the size distribution shifted toward smaller floes and the number of floes increased. Lateral melting causes the distribution to deviate from a power law for small floe sizes.

Limiting diameter of pancake ice

Two mechanisms have been hypothesized to limit the diameter of pancake ice, one due to bending failure and the other due to tensile failure. We conducted two series of laboratory experiments to monitor pancake ice growth from an open water condition in indoor wave tanks. One used urea doped water and the other used salt water with concentration similar to ocean conditions. The final size of the pancakes and the wave conditions are reported here. The laboratory data suggest that in the growth stage, pancake ice floe diameter is limited by tensile failure, in contrast to the bending failure control of floe diameter in ice breakup by waves. The final diameter of the pancake floes is proportional to the wavelength. The proportionality is controlled by wave amplitude and freezing conditions. For wave amplitude A, the proportionality obtained from data agrees closely with the tensile failure theoretical prediction of 1/A0.5.

Wave rafting and the equilibrium pancake ice cover thickness

Pancake ice, the circular floes formed during ice growth in a wave field, forms in many polar and subpolar seas. Vertical thin sections of cores taken from the ice cover in these regions show distinct layering structure. These observations suggest wave rafting could play a significant role in defining the ice cover thickness, much more so than thermodynamic growth. Although wave rafting is intuitively apparent, no previous study relating the resulting ice cover to wave characteristics has been conducted. In this study we utilize both laboratory experiments and numerical simulations to determine the rafting process. We propose a theory that predicts a final equilibrium thickness, provided that the incoming wave is kept constant. The equilibrium thickness from the theory is proportional to the square of the wave amplitude and the square of the floe diameter and is inversely proportional to the cube of the wavelength. This theory relates the final ice cover thickness to the wave characteristics and the size and surface properties of the pancake ice floes. This theory also provides a way to calculate the speed with which the boundary between the single‐layer pancake ice floes and the equilibrium rafted ice cover propagates. We conduct laboratory experiments with plastic model pancake ice to create rafting. We perform computer simulations with a three‐dimensional discrete element model that simulates the movement of disc‐shaped floes in the wave field. We compare the theoretical result with the laboratory experiments and a numerically simulated rafting process. Both the laboratory and the computer simulation results compare favorably with the theory.

The effect of a storm on the 1992 summer sea ice cover of the Beaufort, Chukchi, and East Siberian Seas

For the summer Beaufort, Chukchi, and East Siberian Seas a variety of active and passive microwave satellite data are used to determine the response of the ice edge and interior to a storm. Specifically, the study concentrates on a low‐pressure system that passed over the region between August 14 and 20, 1992, with peak geostrophic winds of about 18 m s−1. Through the use of the ERS‐1 imaging radar and the Special Sensor Microwave/Imager the ice response is examined at two locations: at the ice edge for a nearly stationary location in the Chukchi Sea and in the ice interior along three swaths in the Beaufort, Chukchi, and East Siberian Seas. The ice edge observations show that the storm fractures the large floes into small floes, some of which are advected into the adjacent warm water. The ice interior observations show that the storm caused an increase in the open water amount and a shift in the floe size distribution toward smaller floes. In the ice interior, application of the cumulative number distribution N(d), where N is the number of floes per unit area that are no smaller than some floe diameter d, shows that for d>1 km, N behaves like d−α, where α lies in the range 1.8–2.9. Our analysis also shows that this slope is not affected by the storm and is slightly larger near the ice edge.

A conceptual model for pancake-ice formation in a wave field

AbstractIt is well known that waves jostle frazil-ice crystals together, providing opportunities for them to compact into floes. The shape of these consolidated floes is nearly circular, hence the name: pancakes. From field and laboratory observations, the size of these pancakes seems to depend on the wavelength. Further aggregation of these individual pancakes produces the seasonal ice cover. Pancake-ice covers prevail in the marginal ice zone of the Southern Ocean and along the edges of many polar and subpolar seas. This theoretical paper describes conceptually the formation process of a pancake-ice cover in a wave field. The mechanisms that affect the evolution of the entire ice cover are discussed. Governing equations for the time-rate change of the floe diameter, its thickness and the thickness of the ice-cover are derived based on these mechanisms. Two criteria are proposed to determine the maximum floe size under a given wave condition, one based on bending and the other on stretching. Field and laboratory observations to date are discussed in view of this theory.

Compression of floating ice fields

The compression of ice fields made up of thin floes is central to the processes of ice jam formation in northern rivers, pressure ridge formation in northern seas, and the dynamics of ice fields in Arctic and Antarctic marginal seas. This work describes the results of computer simulations in which a floating layer of circular floes, confined in a rectangular channel, is compressed by a pusher plate moving at a constant speed. The accuracy of the simulations is assessed by comparison with a series of similar physical experiments performed in a refrigerated basin. Following this comparison, the computer model is used to perform an extensive series of simulations to explore the effect of variations in channel length and width, the ratio of floe diameter to thickness, floe on floe friction coefficients, and the distribution of floe diameters on the force required to compress the floes. The results show that reducing the aspect ratio of the floes or increasing the friction coefficient increases the force needed to compress the floes. Both changes increase the force by changing the dominant failure mechanism in the layer of floes from rafting to underturning. Increasing channel width reduced the compressive force (per unit channel width) by reducing the relative importance of frictional drag at the channel edges. Last, the results of a simulation using a distribution of floe diameters was indistinguishable from those of a simulation using floes with a single diameter equal to the average diameter of the distribution.

Air–Ice–Ocean Momentum Exchange. Part II: Ice Drift

A model was constructed to estimate ice floe trajectories. The model considers the balance of atmosphere and ocean drag forces on ice floes, including skin and body drag forces from wind, waves, and currents. Discussion of air–ice and water–ice skin stresses, water–ice form stress, and wave radiation stress is presented. Estimates are presented for the ice drift in a variety of hypothetical situations: (i) as a function of ice floe diameter, thickness, and concentration; (ii) in “wave” and “no wave” situations; and (iii) in constant wind forcing and time-varying wind forcing situations. The model is shown to be consistent with wave and ice observations collected during the Labrador Ice Margin Experiment 1987 on the Grand Banks during relatively high wind situations. Combining this model with the wave-scattering model of Part I allows estimation of 1) the effect of wave scattering attenuation on ice floe trajectories and the ice edge and 2) the effect of ice floe drift on the wave spectra. Thus, an enhanced modeling of wave and ice dynamics is achieved.

Discrete element modelling of a broken ice field — Part II: simulation of ice loads on a boom

A two-dimensional discrete element model which simulates the dynamics and interaction forces between individual ice floes in a broken ice field has been described in the paper “Discrete Element Modelling of a Broken Ice Field — Part I: Model Development”. The present paper elaborates on the application of this model using three examples. The first example presents a simulation of the forces exerted on a boom when it is pulled through a broken ice sheet. This example refers to small-scale tests, in which the kinematic behaviour and calculated forces are compared with, and calibrated against, tests with such a boom in the ice tank at the National Research Council Canada (NRC, Ottawa). The two other examples, utilizing the calibration from the small-scale testing, study the full-scale interaction between a broken ice field and the boom. Example 2 shows that for an ice thickness of 1.0 m and a boom speed of 0.2 m/s, the average forces on a 250 m wide boom were 50 kN and 119 kN for ice concentrations of 0.4 and 0.6, respectively. In Example 2 the floe diameters ranged from 20 m to 36 m. The values of the parameters in the visco-elastic-plastic rheology (linear spring constant, viscous damping coefficient and friction coefficient) appeared to have marginal influence on the force exerted on the boom. The average force increases with increasing ice concentration, ice thickness, boom speed and boom width. Keeping the ice concentration, ice thickness and boom speed fixed, the average force on the boom is proportional to the boom width.

The response of ice floes to ocean waves

A precise linear mathematical theory is reported to model the response of a solitary ice floe in ocean waves, allowing the floe to bend with the passing wave. Both infinite and finite water depths are considered, and the model is also extended to include a pair of separated floes of different length, the case of n‐floes then being a natural and straightforward development. For a single ice floe, perfect transmission is achieved whenever the wavelength beneath the ice couples perfectly to the length of the ice floe. Then the strains induced in the bending ice floe reach a maximum, and because multiple‐cycle tuning can occur in floes which are long compared to the wavelength, strain response amplitude operators (RAOs) are complicated. By considering the case of infinite stiffness, heave and roll RAOs are also found for typical ocean wave periods, and these agree well with two‐dimensional rigid‐body models. Finally, ice floes of different diameters but constant 1‐m thickness are subjected to spectral forcing, and the strain spectral density for each is found. Spectral density envelopes increase gradually with floe diameter, achieving a maximum value for a floe of about 102m. Thereafter strains never decrease below those for the 80‐m curve owing to multiple‐cycle tuning. This may explain the presence of zones within an ice field where floe size never exceeds some prescribed value. Results obtained from the complete theory for two adjacent floes do not differ significantly from those found by applying the single‐floe model serially except when the separation is very small.

Sea ice melting and floe geometry in a simple ice‐ocean model

A coupled sea ice‐ocean numerical model has been developed that addresses the role of floe geometry during summertime melting. The model contains a diagnostic equation for average floe diameter in addition to the usual prognostic equations for ice volume per unit area and ice concentration. The partition between melting on the top, bottom, and lateral (side) surfaces of floes is examined using time‐dependent simulations with differing initial average floe diameters. The different parameterizations for bottom and lateral melting in the literature are also compared and found to vary significantly. The results show that lateral melting is important only for floes with diameters less than O(30 m), given atmospheric thermal forcing typical of the central Arctic in summer. This means that the decrease in ice concentration over the summer is a strong function of floe diameter, in keeping with simple geometrical arguments. In all cases, about 80% of the net thermal energy that enters the ocean through leads goes toward melting ice, while the rest warms the ocean.

The partition of air‐ice‐ocean momentum exchange as a function of ice concentration, floe size, and draft

A coupled sea ice‐ocean model is used to examine the relative magnitudes of terms in the sea ice momentum equation, for ice concentrations less than 100%. This numerical model for steady state, horizontally homogeneous flow includes two terms that have previously been neglected in such quantitative models. These are oceanic form drag and wave radiation pressure, both of which are lateral forces that act on the sides of floes. The former is generally decelerative, while the latter is accelerative. The model accepts as input variables average ice draft, areal concentration, and floe diameter. It is found that form drag can be greater than or of the same order as skin friction drag for small, thick floes at low concentrations. An exception to this rule occurs when the effect of wakes between floes reduces the local form drag. The higher net drag that generally exists at low concentrations implies lower ice floe speeds. Wave radiation pressure is negligible in all cases, although this is sensitive to our choice of fetch parameterization. Ocean drag is often parameterized in numerical models of sea ice as a skin friction term alone, with a constant drag coefficient between ice and (prescribed) geostrophic current velocities. Results from the present model are plotted in terms of such a drag coefficient, which is a function of concentration, floe size, and draft. This could be useful in future work where floe size data become regularly available, for instance, from radar satellite imagery.

Spectral evolution of wind-generated surface gravity waves in a dispersed ice field

The Marginal Ice Zone includes wide areas covered by dispersed ice floes in which wave conditions are significantly affected by the ice. When the wind blows from the solid ice pack, towards the open sea, growing waves are scattered by the floes, and their spectral characteristics modified. To further understand this problem, a model for the evolution of wind waves in a sparse field of ice floes has been developed. The sea state is described by a two-dimensional discrete spectrum. Time-limited wave growth is obtained by numerical integration of the energy balance equation using the exact nonlinear transfer integral. Wave scattering by a single floe is represented in terms of far-field expressions of the diffracted and forced potentials obtained numerically by the Green function method. The combined effect of a homogeneous field of floes on the wave spectrum is expressed in terms of the Foldy–Twersky integral equations under the assumption of single scattering. The results show a strong dependence of the spectrum amplitude and directional properties on the ratio of the ice floe diameter to the wavelength. For a certain range of this parameter, the ice cover appears to be very effective in dispersing the energy; the wave spectrum rapidly tends to isotropy, a tendency which prevents the normal growth of wave energy and the decrease in peak frequency. Therefore, in the Marginal Ice Zone, the ability of an offshore wind to generate a significant wave field is severely limited.

Aggregation and Disaggregation of Fine-Grained Lake Sediments

The effects of fluid shear and sedimentation concentration on the aggregation, and especially disaggregation, of fine-grained sediments in lake waters continues to be an important research area. It has been shown in previous studies that the steady-state median floe size decreases as the shear stress increases and also decreases as the suspended sediment concentration increases. Here, the time rate of change of the particle size distribution as affected by aggregation and disaggregation due to fluid shear and to collisions between particles is considered from a theoretical point of view. Approximate value for the coefficients appearing in the rate equation and their dependence on floe diameter, shear stress, and density were determined. In order to explain the observed decrease in floe size as the sediment concentration increases, the theoretical analysis requires disaggregation due to three-body collisions. The theory does not require disaggregation due to fluid shear. For the present range of parameters, fluid shear seems to have a negligible direct effect on disaggregation, while collisions between particles (possibly due to shear but also due to differential settling and Brownian motion) are the dominant mechanism for disaggregation.