A two-layer flow model to represent ice-ocean interactions beneath Antarctic ice shelves

Abstract. We develop a two-dimensional two-layer flow model that can calculate melt rates beneath ice shelves from ocean temperature and salinity fields at the shelf front. The cavity motion is split into two layers where the upper plume layer represents buoyant meltwater-rich water rising along the underside of the ice to the shelf front, while the lower layer represents the ambient water connected to the open ocean circulating beneath the plume. Conservation of momentum has been reduced to a frictional geostrophic balance, which when linearized provides algebraic equations for the plume velocity. The turbulent exchange of heat and salt between the two layers is modelled through an entrainment rate which is directed into the faster flowing layer.

The numerical model is tested using an idealized geometry based on the dimensions of Pine Island Ice Shelf. We find that the spatial distribution of melt rates is fairly robust. The rates are at least 2.5 times higher than the mean in fast flowing regions corresponding to the steepest section of the underside of the ice shelf close to the grounding line and to the converged geostrophic flow along the rigid lateral boundary. Precise values depend on a combination of entrainment and plume drag coefficients. The flow of the ambient is slow and the spread of ocean scalar properties is dominated by diffusion.