Solidification of leads: approximate solutions of non-linear problem

We present new analytical results relating to the growth and evolution of sea ice. It is noteworthy that thin sea ice plays a central role in the surface heat and mass balance of the Arctic Ocean. In order to describe these balances, we analyze highly resolved temperature data taken through the air/sea/ice interface during the transition from an ice-free to an ice-covered Arctic Ocean surface. Our detailed analysis of the field data is based on the classical model of a mushy layer, which is modified in order to obtain analytical solutions in explicit form (so, for example, ice thickness and growth rate, temperature distributions, conductive and latent heat fluxes are determined). Furthermore, we find that the sea-ice growth is not simply a square-root function of time. It depends on the temperature variations in the atmosphere and lies between two square-root functions of time for the maximum and minimum temperatures found during observations. The theory under consideration is in good agreement with observations.