Fission of Single and Multiple Eddies

Abstract

The analytical results for the splitting conditions of isolated barotropic eddies and the associated final equilibrium state are extended to: 1) nonlinear baroclinic eddies; 2) a group of four nonlinear closely packed eddies, two of which are cyclonic and two of which are anticyclonic (i.e., multiple eddies); and 3) joint nonlinear eddies (i.e., a system consisting of two eddies situated one above the other). The final equilibrium state associated with the group (of four) fission is related to a nonlinear version of geostrophic turbulence and, therefore, is referred to as ageostrophic turbulence.Taking into account that inviscid fission may involve loss of energy via waves radiation, the breakup process is examined by conserving integrated angular momentum, potential vorticity, and mass. The analytical expressions for the conservation of these three properties provide a set of algebraic equations that are solved numerically.For baroclinic eddies embedded in an infinitely deep lower layer, it is found that, as in the barotropic case, only intense cyclones can break up. This result from the fact that, despite the large amplitude of the nonlinear baroclinic eddies, the offspring are still forced a considerable distance away from their original prebirth center of rotation as is the case with the barotropic eddies. This causes a large gain in angular momentum implying that only eddies whose angular momentum is relatively large to begin with are capable of being potential parents. Again, as in the barotropic case, it turns out that only intense cyclones have large enough angular momentum to allow splitting (because the cyclonic orbital speed is in the same direction as the earth's rotation).In ageostrophic turbulence, the cyclones break up and the anticyclones merge. Namely, the fission of the cyclones provides the energy necessary for the fusion of the anticyclones. Hence, the final result is a nonlinear system resembling a "Mickey Mouse" (with one large anticyclone and four small cyclones) whose total energy is identical to the total initial energy prior to the fission.The impossibility of baroclinic anticyclones to break up appears initially to be in contradiction with classical laboratory experiments which show what seems to be an anticyclonic fission. The solution for joint eddies consisting of a cyclone situated above an anticyclone suggests, however, that what really breaks up in the laboratory is the cyclone on top rather than the anticyclone underneath. (Recall that the generation of anticyclones in the laboratory is often accompanied by the formation of a cyclone on top due to convergence.)It is suggested that the impossibility of baroclinic anticyclones to break up and the tendency of cyclones to split may provide an explanation for the relative abundance of anticyclones in the ocean.