A Simple Model of the Ice Shelf-Ocean Boundary Layer and Current

Ocean-forced basal melting has been implicated in the widespread thinning of Antarctic ice shelves, but an understanding of what determines melt rates is hampered by limited knowledge of the buoyancy- and frictionally controlled flows along the ice shelf base that regulate heat transfer from ocean to ice. In an attempt to address this deficiency, a simple model of a buoyant boundary flow, considering only the spatial dimension perpendicular to the boundary, is presented. Results indicate that two possible flow regimes exist: a weakly stratified, geostrophic cross-slope current with upslope flow within a buoyant Ekman layer or a strongly stratified, upslope current with a weak cross-slope flow. The latter regime, which is analogous to the steady solution for a katabatic wind, is most appropriate when the ice-ocean interface is steep. For the gentle slopes typical of Antarctic ice shelves, the buoyant Ekman regime, which has similarities with the case of an unstratified density current on a slope, provides some useful insight. When combined with a background flow, a range of possible near-ice current profiles emerge as a result of arrest or enhancement of the upslope Ekman transport. A simple expression for the upslope transport can be formed that is analogous to that for the wind-forced surface Ekman layer, with curvature of the ice shelf base replacing the wind stress curl in driving exchange between the Ekman layer and the geostrophic current below.