  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
$\mathcal{O}(10^{-5}) \, \rm m^2s^{-1}$.
