Eddy instability and interaction in the ocean play an important role for the vertical transport and mixing of tracers and momentum. We study the dynamics of oceanic eddies with a non-hydrostatic numerical model (HAROMOD). The simulations show a cyclone-anticyclone asymmetry. Centrifugal instability is shown to play an important part in the dynamics of strong anticyclonic eddies and the emergence of an asymmetric vorticity field. We emphasize the importance of the very small scales in the eddy dynamics and quantify the vertical transport and mixing. The importance of non-hydrostatic effects are evaluated. Finally, we discuss the impact of the eddy induced vertical transport on the large scale dynamics of the ocean.