Arctic sea ice is one of the most sensitive components of the Earth’s climate system and acts as a bellwether for the changes in it. The ice cover grows, shrinks, and moves because of its interactions with the atmosphere and the underlying ocean. One of the principal challenges associated with modelling the atmosphere-ice-ocean interactions is the lack of definitive knowledge of the rheological properties of the ice cover at large scales. A systematic study of sea ice dynamics since the 1960s has led to the development of many rheological models, but the predictions from these models are not entirely consistent with observations.
In this talk, I will use tools from kinetic theory to obtain the continuum equations of Arctic sea ice motion starting from the dynamics of a single floe and show that the rheology that emerges from floe-floe interactions is viscous — as conjectured by Reed and Campbell (J. Geophys. Res. 67(1), 281 (1962)). The motion of the floe is principally driven by the wind and ocean currents and by inelastic collisions with the neighbouring floes. A mean-field representation of these collisions is developed, neglecting any changes in the floe thickness due to thermal growth and mechanical deformation. This mean-field representation depends on the state of the ice cover, and is expressed in terms of ice concentration and mean thickness. The resulting Langevin equation for the floe velocity, or the corresponding kinetic equation (Kramers-Chandrasekhar equation) for its probability density, provides a complete description of the floe's motion. I then use the floe-scale dynamics to obtain a continuum description of sea ice motion through a Chapman-Enskog analysis of the Kramers-Chandrasekhar equation. The local equilibrium solution to the kinetic equation is found to be the Laplace distribution, in qualitative agreement with observations. Lastly, I will show that the results from this study resolve a conflict associated with the choice of the value of shear viscosity in previous idealised numerical studies of Arctic sea ice motion.