The role of angular momentum in the splitting of isolated eddies

The question of which oceanic eddies can split and break up is addressed with the aid of two simplified analytical models which rely on the conservation of integrated angular momentum. First, an inviscid barotropic model with an initial round vortex is considered. The conditions necessary for the breakup of the vortex without exchanging angular momentum with its environment are examined. A solution for the final state is obtained without solving for the highly nonlinear transient splitting process. It is found that only cyclonic eddies meet the necessary condition for splitting — anticyclonic eddies can never split, no matter what their structure is. The cyclones are subject to a critical intensity above which breaking is possible and below which splitting is impossible. Specifically, cyclones with relative vorticity higher than f (where f is the (uniform) Coriolis parameter) can split into 2 eddies, whereas cyclones with a vorticity higher than f/3 can split into 3 or 4 vortices. The peculiar asymmetry between anticyclones and cyclones is a result of the conservation of integrated angular momentum. This can be demonstrated by noting that during the splitting process, the newly formed eddies are pushed away from their original center of rotation acquiring planetary torque. Therefore, in order for splitting to occur, the torque of the parent eddy must be large enough to accommodate for this addition of planetary torque. It turns out that only cyclones, which typically have more absolute angular momentum than their anticyclonic counterparts (because they rotate in the same sense as the spin of the earth), have enough torque to allow splitting. The above analysis is also applied to the splitting of a fully nonlinear zero potential vorticity lens. As in the barotropic anticyclonic cases, splitting is strictly impossible because the parent eddy does not have enough angular momentum.