Buoyant meltwater from the sloping base of Antarctica’s ice shelves can become supercooled as it rises if it warms more slowly than the increasing ambient freezing temperature. Within the supercooled water small thin discs of ice, known as frazil or platelet ice, can form a slurry of ice crystals 1–100 µm thick and 1–4 mm in diameter, which nucleate and grow to relieve the supercooling over timescales of hours to days. Once large enough to overcome small-scale turbulent mixing through their own buoyancy, the frazil-ice crystals rise through the water column and become part of an ice platelet matrix along the base of the overlying sea ice or ice shelf. It is likely that in settling out of the water column frazil ice will be heavily influenced by the physics at the ice–ocean boundary, involving a range of processes not considered in most existing models. Here we present results from a new model that incorporates a frazil-ice model within a vertical one-dimensional ocean model. It allows for frazil-ice growth, collision processes, deposition and resuspension from the ice platelet layer at the top of the water column. With this model we explore the conditions required for frazil-ice formation and the net contribution that frazil ice makes to landfast sea ice in McMurdo Sound, Antarctica. A region where frazil and platelet ice are well documented in fast-ice cores, frazil ice is the dominant source of acoustic Doppler current profiler backscatter in the clear waters of the Sound and there is an extensive layer of loose platelets under the fast ice from which ice resuspension has been observed.