Sea ice motion on multiple scales

Arctic sea ice is one of the most sensitive components of the Earth's climate system and acts as a bellwether for 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 work, I will consider the motion of sea ice at three different scales: (i) floe-scale or `microscopic'; (ii) mesoscopic; and (iii) continuum. Starting from the dynamics at the scale of an individual ice floe I will obtain the continuum equations by coarse graining. This approach is similar to the one used to obtain the Navier-Stokes equation from the Boltzmann equation, and allows for the determination of shear viscosity of the ice cover as an explicit function of ice concentration and mean thickness. I will compare results from the theory with observations and idealised simulations and also discuss a more general approach that accounts for phase change and mechanical deformation of ice floes.