Stability of the Viscous-Plastic Sea Ice Rheology

Abstract

The large-scale two-dimensional rheology of a sea ice pack arises from the local contact forces between adjacent does in convergence. It is conventionally modeled by a viscous-plastic constitutive relation to reflect the low or zero stress in a divergent flow field and the rate-independent ridging process in convergence. The authors demonstrate how, for a simple one-dimensional configuration, the elliptical yield curve results in tensile in-plane stresses in divergence that cause a short wave length linear instability. As the ice pack diverges, the ice strength, which is the root cause of the instability, is rapidly reduced, and so, although the model is linearly unstable, it is nonlinearly stable. The practical significance is that the model does not blow up, but systematic grid size-dependent errors associated with the linear instability are introduced throughout the pack. Artificial diffusion terms can be used to prevent the growth of the linear instability. Numerical models must almost always possess artificial diffusion to permit them to run. Here, however, the diffusion is necessary to overcome physical inaccuracies in the model. Diffusion alone is not even a total cure. Generally, diffusive coefficients shrink as a power of the grid size, so as model resolution becomes finer, a previously stable algorithm will become unstable. The problem can be properly posed by constraining the yield curve to lie within the third quadrant of principal stress space.