When seawater becomes supercooled, collections of small ice crystals, known as frazil ice, form and grow. A model of frazil ice dynamics is presented that deals explicitly with the buoyant settling of frazil crystals onto an overlying surface. This yields further insight into transport associated with the ice pump mechanism, whereby ice is melted at depth and transferred to a shallower location as a result of the pressure variation of seawater's freezing temperature. The model is applied to a vertical cross-section through an Ice Shelf Water plume beneath Filchner–Ronne Ice Shelf, Antarctica, and helps to elucidate the depth-variation in its properties for the first time, as well as predicting the precipitation rate of frazil crystals. The model predicts that frazil ice should be preferentially located in a narrow layer near the ice shelf base as a result of the maximum supercooling there and an influx of crystals rising under their own buoyancy. The deposition of these crystals onto the ice shelf is governed by the balance between crystal rising and turbulent transfer of frazil away from the shelf, which is investigated in some detail.