## Iiii

150km

Figure 7. Turbulent background experiments for the (1) straining-out case (r* = 1, 7 =2), (2) merger case (r* = 4, 7 = 2), (3) tripole case (r* =4, 7 = 2), and (4) concentric case (r* =4, 7 = 6). A vorticity clear zone (moat) of 10 km is introduced near the core vortex for the last two experiments.

vorticity of alternate signs, with the whole configuration steadily rotating in the same sense as the vorticity of the elliptically shaped central core (Carton et al., 1989; Polvani and Carton, 1990; Carton and Legras, 1994; Kloosterziel and Carnevale, 1999). Examples of elliptical eyes that might be associated with tripolar vorticity structure were reported by Kuo et al. (1999) for the case of Typhoon Herb (1996) and by Rea-sor et al. (2000) for the case of Hurricane Olivia (1994).

### 4.4. Phase diagrams

DW92 and Dritschel (1995) described the general interaction of two barotropic vortices with equal vorticity but different sizes. The resulting structures can be classified into elastic interaction, merger, and straining-out regimes in terms of the radius ratio r = R1/R2 and the dimensionless gap A/R1. Figure 8, which is reproduced from DW92, summarizes the regimes with the simulated vorticity field in the merger and straining-out regimes. The figure suggests, in general, that binary vortex interaction is prone to produce the merger regime (straining-out regime) if the two vortices are of similar (different) size. Larger separation distances will result in the incomplete merger and incomplete straining-out. The incomplete merger and straining-out regimes result in part of the smaller vortex being torn away incompletely and a tiny vortex being left behind. A separation parameter greater than 1.5 gives elastic interaction. The outer bands in the complete straining-out regime, which result from the smaller vortex, are much too thin to be identified as the outer band of concentric eyewalls. Moreover, there is no tripole regime produced in the end states.

Figure 8. Interaction regimes for binary vortices calculated as a function of the dimensionless gap A/Rl and the vortex radius ratio R2/Rl. The structures are categorized into complete merger, partial merger, complete straining-out, partial straining out and elastic interaction regimes. (Adapted from DW92.)

A/Hi

Figure 8. Interaction regimes for binary vortices calculated as a function of the dimensionless gap A/Rl and the vortex radius ratio R2/Rl. The structures are categorized into complete merger, partial merger, complete straining-out, partial straining out and elastic interaction regimes. (Adapted from DW92.)

Figure 9, adapted from K04, illustrates the Rankine vortex binary interaction regimes as a function of the dimensionless gap A/R1, and the vorticity strength ratio y = Z1 /Z2 for the radius ratios r = Ri/R2 = 1/2,1/3, and 1/4. The abscissa of Fig. 9 is the dimensionless gap A/R 1, which ranges from 0 to 4, and the ordinate is the vorticity strength ratio y, which ranges from 1 to 10. The classifications are based on the scheme devised by DW92 and K04. The structures are categorized into the "concentric," "tripole," "merger," and "elastic interaction" regimes, with the concentric end states shaded. Figure 9 indicates that the tripole vortex structure often serves as the transition between the concentric and merger structures. The results suggest that the formation of a concentric vorticity structure requires: (i) a core vortex with vorticity at least six times stronger than the neighboring vorticity patch; (ii) a neighboring vorticity area that is considerably larger than the core vortex; (iii) a separation distance between the core vortex and the neighboring vorticity patch that is less than three to four times the core vortex radius.

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