The oceanic connections between tidewater glaciers and continental shelf waters are modulated and controlled by geometrically complex fjords. These fjords exhibit both overturning circulations and horizontal recirculations, driven by a combination of water mass transformation at the head of the fjord, variability on the continental shelf, and atmospheric forcing. However, it remains unclear which geometric and forcing parameters are the most important in exerting control on the overturning and horizontal recirculation. To address this, idealized numerical simulations are conducted using an isopycnal model of a fjord connected to a continental shelf, which is representative of regions in Greenland and the West Antarctic Peninsula. A range of sensitivity experiments demonstrate that sill height, wind direction/strength, subglacial discharge strength, and depth of offshore warm water are of first-order importance to the overturning circulation, while fjord width is also of leading importance to the horizontal recirculation. Dynamical predictions are developed and tested for the overturning circulation of the entire shelf-to-glacierface domain, subdivided into three regions: the continental shelf extending from the open ocean to the fjord mouth, the sill-overflow at the fjord mouth, and the plume-driven water mass transformation at the fjord head. A vorticity budget is also developed to predict the strength of the horizontal recirculation, which provides a scaling in terms of the overturning and bottom friction. Based on these theories, we may predict glacial melt rates that take into account overturning and recirculation, which may be used to refine estimates of ocean-driven melting of the Greenland and Antarctic ice sheets.

Bathymetric sills are important features in the ocean-filled cavities beneath a few fast-retreating ice shelves in West Antarctica and northern Greenland. The sills can be high enough to obstruct the cavity circulation and thereby modulate glacial melt rates. This study focuses on the idealized problem of diabatically-driven, sill-constrained overturning circulation in a cavity. The circulation beneath fast-melting ice shelves can generally be characterized by an inflow of relatively warm dense water (with temperatures of a few degrees C above the local freezing point) at depth and cold, less-dense, outflowing water, which exhibits an approximately two-layer structure in observations. We use a two-layer isopycnal hydrostatic model to study the cross-sill exchange of these waters in ice shelf cavities wide enough to be rotationally-dominated. A quasi-geostrophic constraint is determined for the transport imposed by the stratification. Relative to this constraint, the key parameters controlling the transport and its variability are the sill height relative to the bottom layer thickness and the strength of the friction relative to the potential vorticity (PV) gradient imposed by the sill. By varying these two key parameters, we simulate a diversity of flow phenomena. For a given meridional pressure gradient, the cross-sill transport is controlled by sill height beyond a critical threshold in the eddy-permitting, low-friction regime, while it is insensitive to friction in both the low-friction and high-friction regimes. We present theoretical ideas to explain the flow characteristics: a Stommel boundary layer for the friction-dominated regime; mean-eddy PV balances and energy conversion in the low-friction, low-sill regime; and hydraulic control in the low-friction, high-sill regime, with various estimates for transport in each of these regimes.