A series of laboratory experiments were performed in both stratified and homogeneous rotating fluids, with thermal forcing occurring over a semicircular region adjacent to a vertical coastline. The evolution of the flow followed a sequence of events similar to those observed in earlier experiments having no topographic constraints. As the fluid initially adjusts geostropically, a rim current is generated, but it becomes unstable, generating baroclinic eddies that eventually transport fluid out of the convecting region and severely disrupt its dynamics. The sequence of events observed in these laboratory experiments were also observed in a recent set of numerical experiments in a homogeneous ocean with both flat and gently sloping shelves. The magnitude of the rim current observed in both the laboratory and numerical experiments agrees with earlier results obtained in the absence of the coastline. The general shape, structure, and wavelength of the instabilities that can develop on the rim current are similar to those in the earlier unconstrained experiments, although the simulation wavelengths are a little larger. However, if the Rossby radius LR becomes large enough, the formation of the eddies appears to be suppressed so that they apparently play no role in the exchange between shelf and surrounding seas. ¿ 1998 American Geophysical Union