A simple dynamical model for gravity drainage of brine from growing sea ice

Gravity drainage of brine through liquid brine channels is the dominant mechanism for the desalination of growing sea ice. We describe and determine mathematically the essential physics of this process, elucidating the connection between downward flow in brine channels and a convective upward flow in the rest of the porous ice, which we show has a vertically linear structure and strength proportional to a Rayleigh number. Our simple dynamical model of this process is used to interpret the exponential propagation of dye fronts in laboratory experiments. We propose that using our new, derived parameterization for gravity drainage in sea ice in terms of two unknown parameters could lead to computationally feasible improvements to thermodynamic sea-ice models.