Viscous-plastic Rheology Research Articles

Asymptotic Stability of the Viscous–Plastic Sea Ice Rheology

Abstract The stability of the viscous–plastic rheology used extensively to model the dynamics of large–scale sea ice covers is studied. Using energy methods, it is shown that on a bounded domain, the viscous–plastic rheology is asymptotically stable when ocean drag terms are included.

An investigation of the general circulation of the Arctic Ocean using an isopycnal model

A numerical simulation of the general circulation of the Arctic Ocean is presented using Oberhuber's (1993a) coupled sea ice, mixed layer, isopycnal general circulation model (OPYC). The model's novel feature is that the ocean component uses density surfaces as the vertical coordinate. The model domain includes the Arctic Ocean, the Greenland-Iceland-Norwegian (GIN) Sea, and the North Atlantic Ocean. The horizontal resolution is 1.0° in a spherical coordinate system that is rotated with respect to geographical coordinates. The vertical is resolved into eleven isopycnal layers of which the uppermost layer is a turbulent mixed layer. The sea ice is modelled using the dynamic-thermodynamic model of Oberhuber which incorporates the Hibler viscous-plastic rheology. A restriction of the coupled model used here is the artificial placement of solid walls across the Bering Strait and at the equator in the Atlantic Ocean. Monthly climatological atmospheric forcing is used to spin the model into a cyclo-stationary equilibrium. Model results are presented and discussed with respect to observational and previous modelling studies. The simulated water mass properties and circulation are in reasonable agreement with observations. Based on the simulation results, new circulation patterns are suggested for the deep flow within the Arctic Ocean. In particular, it is proposed that for the Atlantic layer and deeper waters there exists a multi-gyre circulation pattern consisting of cyclonic gyres that essentially follow contours of bottom topography. DOI: 10.1034/j.1600-0870.1996.00008.x

A Numerical Simulation of Sea Ice Cover in Hudson Bay

Abstract Hibler's dynamic-thermodynamic sea ice model with viscous-plastic rheology is used to simulate the seasonal cycle of sea ice motion, thickness, compactness, and growth rate in Hudson Bay under monthly climatological atmospheric forcing and a prescribed ocean surface current field. The sea ice motion over most of the domain is driven mainly by the wind stress. Wintertime sea ice velocities are only of the order of 1–5 (× 10−4 m s−1) due to the nearly solid ice cover and the closed boundary constraint of Hudson Bay. However, the velocities rise to 0.10–0.20 m s−1 during the melting and freezing seasons when there is partial ice cover. The simulated thickness distribution in mid–April, the time of heaviest ice cover, ranges from 1.3 m in James Bay to 1.7 m in the northern part of Hudson Bay, which compares favorably with observations. The area-averaged growth rate, computed from the model is 1.5–0.5 cm day−1 from December to March, is negative in May (indicative of melting) and reaches its minimum v...

Simulation of the Atlantic Circulation with a Coupled Sea Ice-Mixed Layer-Isopycnal General Circulation Model. Part I: Model Description

Abstract A diabatic ocean general circulation model based on primitive equations is described. It uses isopycnals as Lagrangian coordinates in the vertical and predicts a free surface. Prognostic fields of temperature and salinity enter the dynamics as active tracers through a realistic equation of state. The surface boundary layer is parameterized by a detailed mixed-layer model. A sea ice model with a viscous-plastic rheology is coupled to the mixed layer. Thermal forcing, wind stress, and surface input of turbulent kinetic energy are determined from monthly mean values of atmospheric quantities, while the freshwater flux still is parameterized by a Newtonian relaxation towards the observed surface salinity. The model equations are written in layer formulation. Each interface represents an isopycnal. As the equations are written in flux form, the mass flux and the content of mass, heat, and salt are conserved in the model domain. A potential vorticity conserving scheme is included. Except for the mixed ...

Visualization Of Marginal Ice Zone Dynamics

Ice floe dynamics in marginal ice zones are simulated using a discrete element model. The ice floes are modelled as random sized, inelastic circular discs floating on the water surface. Contact conditions are represented by a constant restitution and friction coefficients. The ice floes are driven by a uniform wind field. The simulations predict ice floe displacements, rotations, compaction and pressures. This paper focuses on animation and visualization of the simulation output. INTRODUCTION Marginal Ice Zones (MIZ) are broken ice fields which often form at the edge of the polar ice pack, next to open ocean. They form as a result of several processes that take place at the pack ice edge including the incidence of waves and increase of temperatures. A MIZ typically extends over a width of the order of 100 km, and consists of distinct floes with diameters varying from a few meters to several kilometres. Discussions of the morphology and behaviour of MIZ were given by Wadhams [1] and [2], and Lepparanta and Hibler [3]. Models of MIZ dynamics have been developed using a viscous-plastic rheology by Lepparanta and Hibler [4], and a cavitating fluid analogy by Flato and Hibler [5]. The discrete nature of the ice floes has also prompted the use of continuum models of flowing granular materials to treat MIZ (e.g. Shen et al. [6] and Lu et al. [7]). The discrete element approach is used here to simulate MIZ dynamics. This approach has been used to model a variety of problems in Transactions on Information and Communications Technologies vol 5, © 1993 WIT Press, www.witpress.com, ISSN 1743-3517 364 Visualization and Intelligent Design soil and rock mechanics, flow of granular materials, and ice-structure interaction. Some of recent papers on this subject were compiled by Mustoe [8], The present study examines the response of an assembly of ice floes to wind drag, water drag and Coriolis force. Interaction forces between the floes are calculated from an inelastic contact model. The simulation predicts the spatial and temporal distributions of ice velocities, concentrations, trajectories and pressures. Animation of the numerical simulations played an essential role throughout this study. It provided an effective means for debugging and verification of the model. Also with the very large amount of information generated by the simulations, animation was necessary for illustrating the salient trends of MIZ behaviour. The present simulations are based on a model developed by Savage [9]. The following sections briefly discuss the discrete element model of the floes, the equations of motion of individual floes, and the boundary conditions. Presentation of a simulation run follows with emphasis on the animation approach and visualization of the results. DISCRETE MODEL OF ICE FLOES Contact model The ice cover is modelled as an assembly of circular, random sized, inelastic discs. At the contact between two discs, linear loading and unloading springs are used to calculate the normal force as illustrated in Figure 1. The normal force per unit length is given by