A viscous continuum theory of sea ice motion based on stochastic floe dynamics

In this study, we 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., vol. 67 (1), 1962, pp. 281–297). 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 (KCE)) for its probability density, provides a complete description of the floe’s motion. We then use the floe-scale dynamics to obtain a continuum description of sea ice motion through a Chapman–Enskog analysis of the KCE. The local equilibrium solution to the kinetic equation is found to be the Laplace distribution, in qualitative agreement with observations. Our approach also allows us to establish the dependence of pressure and shear viscosity of the ice cover on ice concentration and mean thickness. Lastly, we show that our results resolve a conflict associated with the choice of the value of shear viscosity in previous idealised numerical studies of Arctic sea ice motion.