Thermosolutal convection induced by freezing a layer of seawater from above is studied in a series of numerical experiments. The model equations take into account the dependence of the density and the temperature of maximum density on salt content, the possible presence of penetrative convection and supercooling effects. The threshold Values for the onset of convection are determined over a wide range of parameter space. Two types of cell pattern are predicted by the linear theory : (1) convection of the entire fluid cell and (2) multi-layer convection. An attempt is made at quantifying the cabbeling instability associated with the onset of the latter. Only multi-layer convection prevails for supercritical Rayleigh numbers. For a specific parameter range, a flow pattern consisting of a strongly convecting layer floating between two relatively stable layers is found. The numerical experiments seem to imply that penetrative convection delays the release of heat to the atmosphere during the formation of polynyas.