The time development of a dense eddy placed on a varying topography in a rotating system is the subject of this paper. It is shown that if the bathymetric variations are comparable with the thickness of the eddy, these will induce a first-order time development in the water mass. Large-amplitude geostrophic theory shows that the water is advected along the depth contours with a speed that is proportional to the slope of the bottom. The results are applied to a laboratory experiment with a rotating parabolic channel. According to theory, an initially circular eddy placed in the centre of the channel becomes elliptical while shifting its axis along the channel. The outcome of the experiment is in accordance with theory, and the importance of topographic advection in the ocean is discussed. It is suggested that the mechanism may be important for moving water from deep-water formation sites and into the global deep-water circulation.