We use numerical simulations based on the shallow water equations for a homogeneous fluid on anf-plane to study the evolution of a cyclonic eddy over a topographic slope. The results are compared with analogous simulations using the nondivergent approximation in order to determine the effect of the free-surface vortex stretching terms. The simulations use a geometry and parameters related to the experimental results of Carnevaleet al.(1991). We find that this vortex stretching produces a significant reduction in the eddy speed. Our numerical results are supported by theoretical analyses, largely set in the quasi-geostrophic context.