Simulation of Sea-ice Thermodynamics by a Smoothed Particle Hydrodynamics Method

Abstract The paper deals with the problem of sea-ice pack motion and deformation under the action of wind and water drag forces. Differential equations describing the behaviour of ice, with its very distinct material responses in converging and diverging flows, express the mass and linear momentum balances on a horizontal plane (the free surface of the ocean). The thermodynamic effects (ice melting and lead water freezing) are accounted for by adding source terms to the equations describing the evolution of the ice thickness and area fraction (concentration). These thermodynamic source terms are described by means of a single function that idealizes typical ice growth-rates observed in winter in the Arctic. The equations governing the problem are solved by a fully Lagrangian method of the smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model was used to simulate the flow of a sea-ice pack driven by wind drag stresses and varying seasonal temperatures. The results of numerical simulations illustrate the evolution of an ice pack, including distributions of ice thickness and ice area fraction in space and time for assumed temperature distributions.