Mathematical characteristics of sea ice dynamics models

Abstract

Mathematical characteristics of plasticity models that describe large‐scale sea ice behavior are studied in an attempt to understand the models better and to compare the analytical results to observed ice behavior. Separate stress and velocity characteristics occur when a nonassociated flow rule is used. The two sets coincide for associated flow rules. The relative orientation of characteristic directions at a point can change depending on the stress state and the direction of plastic stretching. Two real velocity characteristic directions exist when the magnitude of shearing exceeds the magnitude of dilating, one exists when they are equal, and none exist when the shearing magnitude is less than the dilating magnitude. The system is hyperbolic, parabolic, or elliptic, respectively, in these conditions. Quasi‐steady elastic‐plastic and viscous‐plastic models have identical characteristics so that we cannot use the characteristics to discriminate between these models. Attention has been focused on the velocity characteristics with the desire to relate these directions directly to leads and other features observed in satellite imagery. The velocity characteristic curves cannot stretch, so that floes lying along a characteristic line neither approach nor separate from each other. Therefore the amount of open water will not change between these floes, which makes it unlikely that we will be able to observe fields of characteristic directions directly in satellite imagery. We have, however, observed velocity discontinuities across large‐scale lead systems, which are special characteristic curves. This result offers a way to use remotely sensed imagery directly to estimate part of the deformation field.