Solitary wave or isolated eddy models are often invoked to explain the longevity of strong nonlinear features in oceans and atmospheres. But when we look at the physics in detail, we find that models of isolated eddies often hinge either on an oversimplification of the dynamics or on constraints which are not appropriate for the observed eddies. In a more complete model, as this study demonstrates, rings (and probably other nonlinear geophysical eddies as well) will interact with their surroundings via Rossby wave radiation, primarily in the barotropic mode. Such wave generation leads to a slow decay of the eddy as energy leaks into the wave field.