BISMG:VickyL

Flow beneath ice shelves
Aim is to model the flow of ocean water into the cavity beneath an ice shelf and its interaction with the overlying ice. We want to capture the effect of intrusions of warm water from the surrounding oceans on the basal melt rate of the ice shelf.

Conceptual model
Melt water from the base of the ice shelf and from the foot of an ice stream is assumed to form a layer adjacent the underside of the shelf. The layer flows along the underside to the shelf's front. As it flows ocean water in the cavity is entrained into the melt-water layer.

Model Assumptions

 * 1) Pressure is assumed hydrostatic.
 * 2) Pressure is continuous across layer interfaces

Work in progress
Suggestions and comments from JCRP meeting (13/11/09):
 * Why is diffusion of scalars (T,S) important near the inflow along the grounding line? Surely the scalar difference is driving the plume?
 * Use the simplified momentum equation derived under the assumption of stationary cavity for the motion of the plume with the moving cavity. We know this equation works. Continuity of the whole cavity is satisfied through the streamfunction. Velocity in the cavity is simply the difference between the depth weighted velocity in the whole cavity calculated from the streamfunction and the plume velocity. Question: can we really justify using a stationary ocean assumption just to calculate the plume dynamics and then ignore it?
 * Why not ignore the pressure gradient due to the base of the ice shelf and force term due to the slope of the ice shelf in plume momentum? These terms exist even if there is no flow beneath the ice shelf - they do not drive motion so they should be ignored. In the above model the pressure gradient and the force due to the slope of the ice shelf is found from the barotropic momentum equation and then substituted into the plume equation. Crucially, this substitution introduces a coupling to the cavity flow through the reduced gravity term. By ignoring the two 'forces' the cavity only influences the plume through entrainment in the thickness and scalar equations. There is a reduced gravity term in the momentum equation for the cavity. Perhaps we could calculate the cavity flow directly and then the plume velocity would be the difference between the depth weighted barotropic and cavity velocities.