A Model to Describe the Response of Arctic Sea Ice

Abstract

In this paper we develop a model for the flow of Arctic sea ice within the context of the theory of interacting continua that takes into account the change of phase between the two constituents, ice and water. After documenting the general balance laws for mass, linear and angular momentum, energy, the second law of thermodynamics and the volume additivity constraint, we discuss the specific constitutive relations that are to be used for the various quantities that appear in the balance laws. Ice is modeled as a non-Newtonian fluid that is a generalization of the usual model due to Glen to take into account the ability of ice to develop normal stress differences in simple shear flow, while water is modeled as a Navier–Stokes fluid. Constitutive relations are discussed for the change of phase, the interaction forces such as the drag, etc. In order to make the problem amenable to analysis, we simplify the governing equations, keeping the quintessential features of the problem of interest in mind.