The evolution of under-ice melt ponds, or double diffusion at the freezing point

In an experimental and theoretical study, we model a phenomenon observed in the summer Arctic, where a fresh-water layer at a temperature of 0°C floats both over a sea-water layer at its freezing point and under an ice layer. Our results show that the ice growth in this system takes place in three phases. First, because the fresh-water density decreases upon supercooling, the rapid diffusion of heat relative to salt from the fresh to the salt water causes a density inversion and thereby generates a high Rayleigh number convection in the fresh water. In this convection, supercooled water rises to the ice layer, where it nucleates into thin vertical interlocking ice crystals. When these sheets grow down to the interface, supercooling ceases. Second, the presence of the vertical ice sheets both constrains the temperature T and salinity s to lie on the freezing curve and allows them to diffuse in the vertical. In the interfacial region, the combination of these processes generates a lateral crystal growth, which continues until a horizontal ice sheet forms. Third, because of the T and s gradients in the sea water below this ice sheet, the horizontal sheet both migrates upwards and increases in thickness. From one-dimensional theoretical models of the first two phases, we find that the heat-transfer rates are 5–10 times those calculated for classic thermal diffusion.