As an idealization of convection near an ice boundary, flows in both salt-stratified and non-stratified liquids generated by a cooled slab of solid material are considered through direct numerical simulation. When the liquid far from the slab is homogeneous, significant convection occurs below the ice and apart from a small boundary layer, hardly no flow appears next to the ice. On the contrary, when the background liquid is stratified through a constant salt gradient, a layered flow appears next to the ice if the thickness of the slab is large enough. The latter flows are of double diffusive origin and have a significant effect on the transport of heat and salt near the ice.