A Lagrangian description of sea ice dynamics using the finite element method

In this work, we present a finite element formulation of sea ice dynamics in the Lagrangian description, which traces sea ice drift and is expected to better simulate some solid-like characters of sea ice. In this formulation the sea ice dynamics and thermodynamics are unified into a first order differential equation set for node drifts, node velocities, element ice volumes and element ice areas. For a simple test problem, this finite element sea ice model was compared with the sea ice model in the Eulerian description using the finite difference method. In another test problem of a hexagonal basin, the equation set was integrated for a time period of 90 days for a very strong test drag force. It is found that the designed strategy of mesh evolution provides enough mobility for sea ice drifts and the numerical method is very stable and efficient. While the Hı́bler’s nonlinear viscous-plastic rheology is used as the physical model, the formulation of the finite element sea ice dynamics in the Lagrangian description presented in this work can be incorporated with any other sea ice rheologies.