The marginal ice zone represents the periphery of the sea ice cover. In this region, the macroscale behaviour of the sea ice results from collisions and enduring contact between ice floes. This configuration closely resembles that of dense granular flows, which have been modelled successfully with the rheology. Here, we present a continuum model based on the rheology that treats sea ice as a compressible fluid, with the local sea ice concentration given by a dilatancy function. We infer expressions for and by nonlinear regression using data produced with a discrete element method (DEM) that considers polygon-shaped ice floes. We do this by driving the sea ice with a one-dimensional shearing ocean current. The resulting continuum model is a nonlinear system of equations with the sea ice velocity, local concentration and pressure as unknowns. The rheology is given by the sum of a plastic term and a viscous term. In the context of a periodic patch of ocean, which is effectively a one-dimensional problem, and under steady conditions, we prove this system to be well-posed, present a numerical algorithm for solving it, and compare its solutions to those of the DEM. These comparisons demonstrate the continuum model's ability to capture most of the DEM results accurately. The continuum model is particularly accurate for ocean currents faster than 0.25 m s; however, for low concentrations and slow ocean currents, the continuum model is less effective in capturing the DEM results. In the latter case, the lack of accuracy of the continuum model is found to be accompanied by the breakdown of a balance between the average shear stress and the integrated ocean drag extracted from the DEM. Since this balance is expected to hold independently of our choice of rheology, this finding indicates that continuum models might not be able to describe sea ice dynamics for low concentrations and slow ocean currents.

This work presents three methods for enforcing tangential velocity boundary conditions for the MEEVC scheme, which was shown to be mass, enstrophy, energy and vorticity conserving scheme in the case of inviscid flow [1]. While the normal velocity component can be strongly imposed in a div-conforming formulation for the velocity field, inclusion of the tangential velocity needs to be set through an appropriate choice of vorticity boundary conditions. Three methods to impose the tangential velocity boundary condition will be discussed: The kinematic Dirichlet formulation, the kinematic Neumann formulation and the dynamic Neumann formulation. The conservation properties of each of the resulting schemes are analyzed and numerical results are shown for the Taylor–Green vortex and for the dipole collision test cases. These confirm that kinematic Neumann vorticity boundary conditions perform best.