Rheology of an Ice-Floe Field

Abstract

The aim of the paper is (1) to develop theory to describe sea ice as a collection of finite-sized floes and (2) to construct a rheology based on this description.Successful sea-ice models have considered the ice to be a two-dimensional continuum with a nonlinear plastic rheology, a two-dimensional yield curve being used to determine the internal ice stresses as functions of the strain-rate (Hibler 1979). In this paper, the shape but not the size of such a yield curve is derived from an idealized picture of floes as moving discs, randomly distributed in a plane. The expected collision rate, which determines the energy loss, is calculated in terms of the average floe size, the areal floe-number density, and the strain-rate. For the case in which the ice strength is low, the dependence of the energy loss upon the strain-rate implies a lens-shaped yield curve, the curved portions being parts of a sine wave. This compares with circular, tear drop-shaped and elliptical yield curves that have been used in sea-ice models to date (Coon 1974, Colony 1976, Hibler 1979). The applicability of the derived yield curve to cases where the ice strength is not low and significant ridging takes place, such as in a continuous ice cover is discussed.