We investigate the effect of wave-eddy interaction and dissipation of internal gravity waves propagating in a coherent meso-scale eddy simulated using a novel numerical model called the Internal Wave Energy Model based on the six-dimensional radiative transfer equation. We use an idealized mean flow structure and stratification, motivated by observations of a coherent eddy in the Canary Current System. In a spin-down simulation using the Garret-Munk model spectrum as initial conditions, we find that wave energy decreases at the eddy rim. Lateral shear leads to wave energy gain due to a developing horizontal anisotropy outisde the eddy and at the rim, while vertical shear leads to wave energy loss which is enhanced at the eddy rim. Wave energy loss by wave dissipation due to vertical shear dominates over horizontal shear. Our results show similar behaviour of the internal gravity wave in a cyclonic as well as an anticyclonic eddy. Wave dissipation by vertical wave refraction occurs predominantly at the eddy rim near the surface, where related vertical diffusivities range from $\kappa \approx \mathcal{O}(10^{-7})$ to $\mathcal{O}(10^{-5}) \, \rm m^2s^{-1}$.
