The mechanics of eddy transport from one hemisphere to the other

Abstract The trajectory of a dense eddy that propagates along the bottom of a meridional channel of parabolic cross-section from the Southern to the Northern Hemisphere is described by a twodegrees-of-freedom, Hamiltonian, system. Two simplified types of motion exist in which to first order the meridinal acceleration vanishes. In mid-latitudes the motion is geostrophic, poleward (equatorward) directed along the channel's west (east) flank. On the other hand, right on the equator the motion is describable by linear oscillations along the potential-well generated by the channel's parabolic bottom cross-section. The propagation speed along the equator is much larger than that in mid-latitudes, which enhances the eddy's dissipation via its mixing with overlying ocean water. For motions that occur slightly off the equator the eastward segment is stable while the westward segment is unstable so an expulsion from the equatorial regime takes place during the latter. A dense eddy that arrives near the equator along the channel's west flank has to cross the channel to its east flank where it can either oscillate back (westward) to the other side of the channel or move poleward from the equator along the channel's east flank. The eddy's dissipation during the equatorial part of its trajectory is very large and the probability of the dissipated eddy leaving the equator to either of the two Hemispheres is identical. The non-integrability of the system manifests itself in the sensitive combination of the equatorial, and the mid-latitude, regimes that renders the dynamics of the transport of AABW eddies to the Northern Hemisphere -chaotic. This description explains both the sharp decrease in the amount of AABW water mass in the immediate vicinity of the equator in the Western Atlantic Ocean and the "splitter" effect of the equator encountered in numerical simulations