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A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a ux of energy from the vortex into the wave eld. Using a simply shelf geometry, we determine analytic expressions for the wave wake and the leading order ux of wave energy. By considering the balance of energy between the vortex and wave eld, this energy ux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for nding these nonlinear solutions and examine the parameter dependence of their structure.