A reduced-gravity model for a dense bottom layer under a motionless deep layer is used to investigate bottom layer flow with topography. The two competing effects in the model are topography, which introduces a topographic beta effect, and strong layer thickness variation, which allows for the possibility of zero-layer thickness or grounding. The goal is to arrive at a simple, observationally relevant characterization of the model which can help to distinguish different dynamical mechanisms operating in the ocean. Several regimes are identified, including situations for which the layer depth goes to zero with and without topography. Ways of distinguishing observationally between competing effects are suggested. The study is motivated by the observed shift of Antarctic Bottom Water in the western North Atlantic Ocean from the west to the east; this phenomenon is used to discriminate key elements of the model.