Supercooled convective instability driven by double diffusion and ice crystal growth

In the polar oceans in winter, a combination of cooling, ice growth and brine rejection creates water masses close to the insitu freezing point. We investigate the potential for convection at the base of the mixed layer driven by differential diffusion of heat and salt, supercooling and ice crystal growth, in conditions where both of the temperature and salinity stratifications are statically stable. We consider an initially warmer, fresher layer of salt water overlying a cold, salty layer, but with both at their salinity-dependent freezing temperature. A theoretical model is developed for energy and salt transfer allowing for ice crystal growth, in a limit with plentiful nucleation sites and rapid quenching of supercooling to a state of local thermodynamic equilibrium. Taking the asymptotic limit of small deviations in salinity, the resulting solutions show that rapid diffusive cooling leads to ice crystal growth at the base of the upper layer. We describe flow using the Bousinesq Navier-Stokes equations with a mixture density depending on temperature, salinity and ice concentration, and use a linear stability analysis is to determine the characteristic time and length scales for the onset of convection across a range of ocean salinities.