A NUMERICAL STUDY OF ANISOTROPIC, LOW-REYNOLDS-NUMBER, FREE-SURFACE FLOW FOR ICE-SHEET MODELING

Few ice sheet flow models have been developed that solve the complete set of mechanical equations. Until now, these models were limited to i sotropic conditions. We present here a two-dimensional, finite differe nce method capable of solving the equations for the steady flow of a v iscous, incompressible, anisotropic fluid with a free surface under is othermal conditions. It is not a standard method, especially with resp ect to the time discretization of the numerical scheme, and converges for very low Reynolds numbers. This method is applied here to the plan ar flow of anisotropic ice over flat or irregular bedrock, with no-sli p boundary conditions at the ice-bedrock interface. The results are pr esented here for Newtonian behavior in the vicinity of an ice divide. The ice is assumed to be isotropic at the ice sheet surface, with cont inuous and prescribed development of anisotropy with increasing depth. Going from isotropic to anisotropic situations, our results indicate that the free surface becomes flatter and the shear strain rates large r and more concentrated near the bedrock. The flow is less sensitive t o variations of the bedrock topography in the anisotropic case than in the isotropic case. Furthermore, a new phenomenon appears in the anis otropic case: the partial stagnation of ice in the holes of the bedroc k. These effects have significant consequences when dating the; ice. T he isochrones obtained in the anisotropic case are flatter and the ani sotropic ice is more than 10% younger above the bumps and more than 10 0% older within the holes than for the isotropic ice.