  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 flux of energy from the
vortex into the wave field. Using a simply shelf geometry, we determine
analytic expressions for the wave wake and the leading order flux of wave
energy. By considering the balance of energy between the vortex and wave field,
this energy flux 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
finding these nonlinear solutions and examine the parameter dependence of their
structure.
