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Figure 5. Time dependence of kinetic energy, enstro-phy, and palinstrophy with respect to their initial values for experiments with the vorticity strength ratio (y = 5), skirt parameter (a = 1), vortex radius ratio r =1/3 and the dimensionless gap A/Ri = 2.5. The diffusivity v employed are 3.25 m2 s~1 and 6.5 m2s _1. Note that the palinstrophy (kinetic energy and enstrophy) scale is in the left (right) ordinate. The curves with higher values are the 3.25 m2 s~1 case.

enstrophy is selectively decayed over kinetic energy in two-dimensional turbulence (Cushman-Roisin, 1994). One of the important implications of selective decay is merger dynamics. That is, on the average, the vortices become larger, stronger, and fewer.

Merger dynamics can be understood with the following argument. In the presence of strong rotation, the wind field is nearly geostrophic, so that g^Ap fo I '

to (7) with constant f0 and g* values (i.e. the heating/cooling does not alter the stratification appreciately), requires that Ap/l remain approximately constant. This implies that a steady increase or decrease of the length scale l should be associated with a proportional increase or decrease in the eddy amplitude Ap. The cascade of enstrophy according to (8), along with the conservation of kinetic energy (7), imply a steady increase of the spatial scale l, with a proportional increase in Ap. There is thus a natural tendency toward larger structures in two-dimensional turbulence with successive eddy mergers. Figure 6 shows the evolution of turbulent vorticity fields with initial spatial scales of 5-10 km (r* = 1) and 30-40 km (r* = 4). It is a striking fact that for the random initial state of different scales, a two-dimensional fluid will rapidly organize itself into a system of coherent, interacting vortices swimming through a sea of passive filamentary structure produced from earlier vortex interactions (McWilliams, 1984). To conserve angular momentum and/or kinetic energy during the merger process, the inward merger of the vorticity field toward the core vortex must be accompanied also by some outward vorticity redistribution (Schubert et al., 1999). The outward redistribution can be seen in the form of filaments that orbit the core vortex. The coherent vorticity structures, such as the concentric vortex in Fig. 3, can prolong the merger process into a monopole.

the kinetic energy is p 2 ,VApV

and the enstrophy is g^Ap fo I

where Ap is the pressure perturbation, g* is the reduced gravity, and l is the vortex scale. The near conservation of kinetic energy, according

4.3. Concentric eyewall formation solely from a turbulent background

Given the fact that there is a natural tendency toward larger structures in two-dimensional turbulence with successive eddy mergers, we now address the question of whether the rapid development of a strong vortex within a turbulent background vorticity field can lead to concentric vorticity patterns similar to those observed during binary vortex interactions. Rankine-type u ~

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