Formation of an aggregate scale in Arctic sea ice

The ice pack covering northern seas is a mixture of thick ridged and rafted ice, undeformed ice, and open water. Conventional Eulerian Arctic sea ice models use a plastic yield surface to characterize the constitutive behavior of the pack. An alternative is to adopt a discontinuous Lagrangian approach and explicitly model the formation of leads and pressure ridges. We use a Lagrangian ice model that consists of thousands of discrete polygonal floes 1-4 km in width. At the beginning of a simulation the ice floes are frozen together in a square domain. We apply a linearly varying wind stress that deforms the pack by stretching the viscous-elastic joints between adjacent floes. Fractures propagate along joints forming a crack pattern in the model ice pack. The crack pattern defines a system of large plates 10-100 km in width that are aggregates of many individual floes. The average size of the plates is determined by a competition between the rate of crack creation and the speed of the relaxation wave that travels outward from a newly broken joint and reduces stresses in the surrounding pack. Simulation results are used to characterize the formation of the aggregate structure and to determine how the rate of crack creation and the average area of the aggregate plates depends on tensile strength, the wind stress gradient, and the size of the individual floes. After the formation of the aggregate-scale plate structure, subsequent deformation occurs at the plate boundaries. Since the usual state of the ice pack is a state of failure, an interesting situation is created in which the initial wind-driven deformation creates the material conditions or aggregate structure under which subsequent deformation occurs.