scholarly journals Non-normal flow rules affect fracture angles in sea ice viscous–plastic rheologies

2021 ◽  
Vol 15 (6) ◽  
pp. 2873-2888
Author(s):  
Damien Ringeisen ◽  
L. Bruno Tremblay ◽  
Martin Losch
Keyword(s):  
Sea Ice ◽  
Axial Compression ◽  
Yield Curve ◽  
Axial Loading ◽  
The Arctic ◽  
Flow Rule ◽  
Normal Flow ◽  
Fracture Deformation ◽  
Plastic Potential ◽  
Ice Model

Abstract. The standard viscous–plastic (VP) sea ice model with an elliptical yield curve and a normal flow rule has at least two issues. First, it does not simulate fracture angles below 30∘ in uni-axial compression, in contrast with observations of linear kinematic features (LKFs) in the Arctic Ocean. Second, there is a tight, but unphysical, coupling between the fracture angle, post-fracture deformation, and the shape of the yield curve. This tight coupling was identified as the reason for the overestimation of fracture angles. In this paper, these issues are addressed by removing the normality constraint on the flow rule in the standard VP model. The new rheology is tested in numerical uni-axial loading tests. To this end, an elliptical plastic potential – which defines the post-fracture deformations, or flow rule – is introduced independently of the elliptical yield curve. As a consequence, the post-fracture deformation is decoupled from the mechanical strength properties of the ice. We adapt Roscoe's angle theory, which is based on observations of granular materials, to the context of sea ice modeling. In this framework, the fracture angles depend on both yield curve and plastic potential parameters. This new formulation predicts accurately the results of the numerical experiments with a root-mean-square error below 1.3∘. The new rheology allows for angles of fracture smaller than 30∘ in uni-axial compression. For instance, a plastic potential with an ellipse aspect ratio smaller than 2 (i.e., the default value in the standard viscous–plastic model) can lead to fracture angles as low as 22∘. Implementing an elliptical plastic potential in the standard VP sea ice model requires only small modifications to the standard VP rheology. The momentum equations with the modified rheology, however, are more difficult to solve numerically. The independent plastic potential solves the two issues with VP rheology addressed in this paper: in uni-axial loading experiments, it allows for smaller fracture angles, which fall within the range of satellite observations, and it decouples the angle of fracture and the post-fracture deformation from the shape of the yield curve. The orientation of the post-fracture deformation along the fracture lines (convergence and divergence), however, is still controlled by the shape of the plastic potential and the location of the stress state on the yield curve. A non-elliptical plastic potential would be required to change the orientation of deformation and to match deformation statistics derived from satellite measurements.

scholarly journals Non-normal flow rules affect fracture angles in sea ice viscous-plastic rheologies

2020 ◽  
Author(s):  
Damien Ringeisen ◽  
L. Bruno Tremblay ◽  
Martin Losch
Keyword(s):  
Sea Ice ◽  
Yield Curve ◽  
Confining Pressure ◽  
The Arctic ◽  
Flow Rule ◽  
Normal Flow ◽  
Loading Test ◽  
Fracture Angle ◽  
Plastic Potential ◽  
Ice Model

Abstract. The standard viscous-plastic (VP) sea ice model with an elliptical yield curve and normal flow rule does not simulate fracture angles below 30° in uni-axial compression, in stark contrast with observations of Linear Kinematic Features (LKFs) in the Arctic Ocean. In this paper, we remove the normality constraint in the standard VP model and study its impact on the fracture angle in a simple uni-axial compressive loading test. To this end, we introduce a plastic potential independent of the yield curve that defines the post-fracture deformations or flow rule. The numerical experiments show that the fracture angle strongly depends on the flow rule details. For instance, a plastic potential with an ellipse aspect ratio smaller than that of the standard ellipse gives fracture angles that are as low as 22°. A newly adapted theory – based on one developed from observations of granular material – predicts numerical simulations of the fracture angles for plastic materials with a normal or non-normal flow rule with a root-mean-square error below 1.3°. Implementing an elliptical plastic potential in the standard VP sea ice model requires only minor modifications. The modified rheology, however, takes longer to solve numerically for a fixed level of numerical convergence. In conclusion, the use of a plastic potential addresses several issues with the standard VP rheology: the fracture angle can be reduced to values within the range of satellite observations and it can be decoupled from the exact shape of the yield curve. Furthermore, a different plastic potential function will be required to change the post-fracture deformation along the fracture lines (convergence or divergence) and to make the fracture angle independent on the confining pressure (as in observations).

scholarly journals Modeling Sea Ice fracture at very high resolution with VP rheologies

2018 ◽  
Author(s):  
Damien Ringeisen ◽  
Nils Hutter ◽  
Martin Losch ◽  
L. Bruno Tremblay
Keyword(s):  
Shear Strength ◽  
High Resolution ◽  
Sea Ice ◽  
Granular Materials ◽  
Yield Curve ◽  
Confining Pressure ◽  
Shear Resistance ◽  
Flow Rule ◽  
Normal Flow ◽  
Strength Parameters

Abstract. Recent high resolution pan-Arctic sea ice simulations show fracture patterns (Linear Kinematic Features – LKFs) that are typical of granular materials but with intersection (fracture) angles wider than those observed from high-resolution satellite images (with a modal value of θ = 20°). In this article, We investigate the mechanism of formation and parameter dependencies of ice fracture in simple numerical bi-axial test on a 8 km x 25 km ice floe at an unprecedented resolution of 25m for two different yield curves: an elliptical (VP) and a Coulombic yield curve both with normal flow rule. In the standardVP model, the simulated angle of fracture is θ = 33.9°, compared to 20° in observations. The dependence of the angle of fracture on the ice shear strength is also contrary to that of typical granular materials with larger angle of fracture for higher shear strength – think of a wet sand castle with steeper walls than a dry sand castle. In this model, the divergence along the fracture lines (or LKFs) is entirely dictated by the ice shear strength used in the model with high shear strength resulting in convergence along LKFs and low shear strength resulting in divergence along LKFs. This is again contrary to typical granular materials where divergence (or dilation) is linked with the orientation of contacts normals that oppose the flow with divergence present for larger shear resistance and convergence for lower shear resistance. Moreover, the angle of fracture depends on the confining pressure in the uni-axial test with more convergence as the confining pressure increases, again contrary to granular material that have an angle of fracture that is independent of the confining pressure. We note that all three behaviors of the VP model are linked with the use of an associative (normal) flow rule. In the Coulombic model, the angle of fracture is smaller (θ = 23.5°), but the solution is unstable when the compressive stresses are too large because of the discontinuity between the straight limbs of the yield curve and the elliptical capping. Our results show that while the VP model gives angles of fracture that are visually correct, the bias in the magnitude of the angle of fracture and the physical dependencies of the angle of fracture on mechanical strength parameters and stress fields couple the sea ice mechanical strength parameters, the sea-ice drift, sea-ice deformation (strain-rate) field in an inconsistent way. We consider this evidence to move away from the elliptical yield curve and associative (normal) flow rule, a deformation law that is not applicable to pressure-sensitive and dilatant granular material such as sea ice.

scholarly journals The material properties of ice bridges in the Maxwell Elasto-Brittle rheology

2019 ◽  
Author(s):  
Mathieu Plante ◽  
Bruno Tremblay ◽  
Martin Losch ◽  
Jean-François Lemieux
Keyword(s):  
Sea Ice ◽  
Material Properties ◽  
The Arctic ◽  
Flow Rule ◽  
Narrow Channels ◽  
Angle Of Internal Friction ◽  
Ice Conditions ◽  
Ice Strength ◽  
Short Time ◽  
Ice Model

Abstract. The shape and break-up of landfast ice arches in narrow channels depend on the material properties of the sea-ice. The effect of the material parameters on ice arches in a sea ice model with the Maxwell Elasto-Brittle (MEB) rheology is investigated. The MEB rheology, which includes a damage parameterization, is implemented using the numerical framework of a Viscous-Plastic model. This configuration allows to study their different physics independently of their numerical implementation. Idealized ice bridge simulations show that the elastic part of the model together with the damage parameterization allows the propagation of fractures in space at very short time-scales. The fractures orientation is sensitive to the chosen angle of internal friction, but deviates from theory. It is speculated that these deviations stem from the absence of a flow rule in the rheology. Downwind of a channel, the MEB model easily forms ice arches and sustains an ice bridge. Using a material cohesion in the range of 15–21 kPa is most consistent with the ice bridges commonly observed in the Arctic. Upstream of the channel, the formation of ice arches is complicated by the absence of a relationship between the ice strength and the ice conditions, and by the presence of numerical errors associated with the damage parameterization. Results suggest that the formation of ice arches upwind of a channel is highly dependent on the rheology and calls for more analysis to determine the necessary conditions for their formation.

scholarly journals Analytical Study of an Isotropic Viscoplastic Sea Ice Model in Idealized Configurations

2015 ◽  
Vol 45 (2) ◽  
pp. 331-354 ◽  
Author(s):  
Jérôme Sirven ◽  
Bruno Tremblay
Keyword(s):  
Sea Ice ◽  
Compressive Stress ◽  
Large Scale ◽  
Yield Curve ◽  
Initial Conditions ◽  
Analytic Solutions ◽  
Flow Rule ◽  
Large Area ◽  
Plastic Regime ◽  
Ice Model

AbstractAnalytic solutions of a mechanical sea ice model are computed in idealized configurations. They are then used to study the properties of this model. It classically assumes that the ice behaves at large scale as an isotropic viscoplastic medium. The plastic regime is characterized by a Mohr–Coulomb yield curve. The flow rule corresponds to the one used in granular mediums and depends on a parameter δ that characterizes the expansion properties of the medium. Using simple model configurations, this study first shows that a sliding of the ice along the coast must be permitted; otherwise, the model generally has no solution when the plastic regime is active. This study then shows that the viscous regime is reached only if the stress remains nearly uniform over a large area. For a stress having no particular properties, the plastic regime acts everywhere. In this case, the compressive stress may reach the maximum value allowed by the model close to the coastline. The extension of the domain where the compressive stress is at its maximum depends on δ and the direction of the forcing field. Over this domain, the ice behaves as a fluid material with a small negative viscosity. Last, the authors found that neither the existence of the solution nor its unicity are guaranteed in this stationary model. This result does not imply that the unicity is lost in the transient problem; it suggests that the evolution of sea ice depends not only on the forcing, but also on the initial conditions or history of the system.

scholarly journals Simulating intersection angles between conjugate faults in sea ice with different viscous–plastic rheologies

2019 ◽  
Vol 13 (4) ◽  
pp. 1167-1186 ◽  
Author(s):  
Damien Ringeisen ◽  
Martin Losch ◽  
L. Bruno Tremblay ◽  
Nils Hutter
Keyword(s):  
Shear Strength ◽  
High Resolution ◽  
Sea Ice ◽  
Granular Material ◽  
Yield Curve ◽  
Confining Pressure ◽  
Arctic Sea Ice ◽  
Flow Rule ◽  
Normal Flow ◽  
Loading Test

Abstract. Recent high-resolution pan-Arctic sea ice simulations show fracture patterns (linear kinematic features or LKFs) that are typical of granular materials but with wider fracture angles than those observed in high-resolution satellite images. Motivated by this, ice fracture is investigated in a simple uni-axial loading test using two different viscous–plastic (VP) rheologies: one with an elliptical yield curve and a normal flow rule and one with a Coulombic yield curve and a normal flow rule that applies only to the elliptical cap. With the standard VP rheology, it is not possible to simulate fracture angles smaller than 30∘. Further, the standard VP model is not consistent with the behavior of granular material such as sea ice because (1) the fracture angle increases with ice shear strength; (2) the divergence along the fracture lines (or LKFs) is uniquely defined by the shear strength of the material with divergence for high shear strength and convergent with low shear strength; (3) the angle of fracture depends on the confining pressure with more convergence as the confining pressure increases. This behavior of the VP model is connected to the convexity of the yield curve together with use of a normal flow rule. In the Coulombic model, the angle of fracture is smaller (θ=23∘) and grossly consistent with observations. The solution, however, is unstable when the compressive stress is too large because of non-differentiable corners between the straight limbs of the Coulombic yield curve and the elliptical cap. The results suggest that, although at first sight the large-scale patterns of LKFs simulated with a VP sea ice model appear to be realistic, the elliptical yield curve with a normal flow rule is not consistent with the notion of sea ice as a pressure-sensitive and dilatant granular material.

scholarly journals Observations and Simulations of Meteorological Conditions over Arctic Thick Sea Ice in Late Winter during the Transarktika 2019 Expedition

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 174
Author(s):  
Günther Heinemann ◽  
Sascha Willmes ◽  
Lukas Schefczyk ◽  
Alexander Makshtas ◽  
Vasilii Kustov ◽  
...  
Keyword(s):  
Sea Ice ◽  
Climate Models ◽  
Climate Model ◽  
Regional Climate ◽  
Open Water ◽  
The Arctic ◽  
Late Winter ◽  
Good Representation ◽  
Hourly Temperature ◽  
Ice Model

The parameterization of ocean/sea-ice/atmosphere interaction processes is a challenge for regional climate models (RCMs) of the Arctic, particularly for wintertime conditions, when small fractions of thin ice or open water cause strong modifications of the boundary layer. Thus, the treatment of sea ice and sub-grid flux parameterizations in RCMs is of crucial importance. However, verification data sets over sea ice for wintertime conditions are rare. In the present paper, data of the ship-based experiment Transarktika 2019 during the end of the Arctic winter for thick one-year ice conditions are presented. The data are used for the verification of the regional climate model COSMO-CLM (CCLM). In addition, Moderate Resolution Imaging Spectroradiometer (MODIS) data are used for the comparison of ice surface temperature (IST) simulations of the CCLM sea ice model. CCLM is used in a forecast mode (nested in ERA5) for the Norwegian and Barents Seas with 5 km resolution and is run with different configurations of the sea ice model and sub-grid flux parameterizations. The use of a new set of parameterizations yields improved results for the comparisons with in-situ data. Comparisons with MODIS IST allow for a verification over large areas and show also a good performance of CCLM. The comparison with twice-daily radiosonde ascents during Transarktika 2019, hourly microwave water vapor measurements of first 5 km in the atmosphere and hourly temperature profiler data show a very good representation of the temperature, humidity and wind structure of the whole troposphere for CCLM.

scholarly journals On the effect of rheology on seasonal sea-ice simulations

1991 ◽  
Vol 15 ◽  
pp. 17-25 ◽  
Author(s):  
Chi F. Ip ◽  
William D. Hibler ◽  
Gregory M. Flato
Keyword(s):  
Shear Stress ◽  
Sea Ice ◽  
Correlation Coefficients ◽  
Arctic Basin ◽  
The Arctic ◽  
Flow Rule ◽  
Average Model ◽  
Ice Drift ◽  
Cavitating Fluid

A generalized numerical model which allows for a variety of non-linear rheologies is developed for the seasonal simulation of sea-ice circulation and thickness. The model is used to investigate the effects (such as the role of shear stress and the existence of a flow rule) of different rheologies on the ice-drift pattern and build-up in the Arctic Basin. Differences in local drift seem to be closely related to the amount of allowable shear stress. Similarities are found between the elliptical and square cases and between the Mohr-Coulomb and cavitating fluid cases. Comparisons between observed and simulated buoy drift are made for several buoy tracks in the Arctic Basin. Correlation coefficients to the observed buoy drift range from 0.83 for the cavitating fluid to 0.86 for the square rheology. The average ratio of buoy-drift distance to average model-drift distance for several buoys is 1.15 (square), 1.18 (elliptical), 1.30 (Mohr-Coulomb) and 1.40 (cavitating fluid).

scholarly journals Simulation of Snow on Arctic Sea Ice Using a Coupled Snow–Ice Model

2010 ◽  
Vol 11 (1) ◽  
pp. 199-210 ◽  
Author(s):  
Yi-Ching Chung ◽  
Stéphane Bélair ◽  
Jocelyn Mailhot
Keyword(s):  
Sea Ice ◽  
Arctic Ocean ◽  
Snow Depth ◽  
Single Layer ◽  
Coupled System ◽  
The Arctic ◽  
Ice Thickness ◽  
The Arctic Ocean ◽  
Snow Model ◽  
Ice Model

Abstract The new Recherche Prévision Numérique (NEW-RPN) model, a coupled system including a multilayer snow thermal model (SNTHERM) and the sea ice model currently used in the Meteorological Service of Canada (MSC) operational forecasting system, was evaluated in a one-dimensional mode using meteorological observations from the Surface Heat Budget of the Arctic Ocean (SHEBA)’s Pittsburgh site in the Arctic Ocean collected during 1997/98. Two parameters simulated by NEW-RPN (i.e., snow depth and ice thickness) are compared with SHEBA’s observations and with simulations from RPN, MSC’s current coupled system (the same sea ice model and a single-layer snow model). Results show that NEW-RPN exhibits better agreement for the timing of snow depletion and for ice thickness. The profiles of snow thermal conductivity in NEW-RPN show considerable variability across the snow layers, but the mean value (0.39 W m−1 K−1) is within the range of reported observations for SHEBA. This value is larger than 0.31 W m−1 K−1, which is commonly used in single-layer snow models. Of particular interest in NEW-RPN’s simulation is the strong temperature stratification of the snowpack, which indicates that a multilayer snow model is needed in the SHEBA scenario. A sensitivity analysis indicates that snow compaction is also a crucial process for a realistic representation of the snowpack within the snow/sea ice system. NEW-RPN’s overestimation of snow depth may be related to other processes not included in the study, such as small-scale horizontal variability of snow depth and blowing snow processes.

scholarly journals Impact of ocean circulation on regional polar climate simulations using the Arctic Region Climate System Model

1997 ◽  
Vol 25 ◽  
pp. 203-207 ◽  
Author(s):  
David A. Bailey ◽  
Amanda H. Lynch ◽  
Katherine S. Hedström
Keyword(s):  
Sea Ice ◽  
Mixed Layer ◽  
Climate Models ◽  
Regional Climate ◽  
The Arctic ◽  
Water Runoff ◽  
Polar Regions ◽  
Ice Dynamics ◽  
Climate System Model ◽  
Ice Model

Global climate models have pointed to the polar regions as very sensitive areas in response to climate change. However, these models often do not contain representations of processes peculiar to the polar regions such as dynamic sea ice, permafrost, and Arctic stratus clouds. Further, global models do not have the resolution necessary to model accurately many of the important processes and feedbacks. Thus, there is a need for regional climate models of higher resolution. Our such model (ARCSy M) has been developed by A. Lynch and W. Chapman. This model incorporates the NCAR Regional Climate Model (RegCM2) with the addition of Flato–Hibler cavitating fluid sea-ice dynamics and Parkinson–Washington ice thermodynamic formulation. Recently work has been conducted to couple a mixed-layer ocean to the atmosphere–ice model, and a three-dimensional (3-D) dynamical ocean model, in this case the S-Coordinate Primitive Equation Model (SPEM), to the ice model. Simulations including oceanic circulation will allow investigations of the feedbacks involved in fresh-water runoff from sea-ice melt and sea-ice transport. Further, it is shown that the definition of the mixed-layer depth has significant impact on ice thermodynamics.

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