At the margins of the Greenland and Antarctic ice sheets warmer ocean temperatures triggered a retreat, speedup and thinning of numerous marine-terminating glaciers and ice shelves. The flow of warm subsurface waters toward the glaciers and ice shelves is steered by the bathymetry of the continental shelves surrounding Greenland and Antarctica. In Northeast Greenland the 79 North Glacier has Greenland's largest floating ice tongue. A unique data set comprising bathymetric, hydrographic, and current velocity observations obtained at the calving front of the 79 North Glacier emphasizes the importance of the complex bathymetry for the heat transport into the sub-ice cavity. A narrow strait steers the flow of waters exceeding 1°C toward the calving front. Warm waters spilling over a sill and Froude numbers peaking at 1.1 point to a hydraulically controlled flow into the sub-ice cavity. By mixing with glacial meltwater (i.e., both basal meltwater and subglacial runoff), waters inside the cavity are cooled by 0.9°C and freshened by 0.4 generating a shallow outflow of glacially modified waters. Thus, the sub-ice cavity circulation is characterized by a negatively buoyant gravity plume and a positively buoyant ice-shelf plume. Both processes lead to turbulent entrainment and are important drivers for the overturning inside the cavity. Topographic control may constrain the overturning circulation by limiting the amount of warm waters supplied to the grounding line of the floating ice tongue. Although the topographic settings that shape this ice shelf-ocean system are quite specific, the results obtained here may be applied to comparable settings in Northern Greenland and Antarctica.