Vortex interactions and the barotropic aspects of concentric eyewall formation

A new parameter, the vorticity strength ratio, has been added to the Dritschel-Waugh binary vortex interaction classification scheme with the modified Rankine vortices. Specifically, we consider the binary interaction between a small and strong modified Rankine vortex (the tropical cyclone core with vorticity skirts) and a large and weak vortex nearby. Variation of this parameter leads to end states classified as concentric vorticity structure, tripole vortex structure, and multiple eyewall structure. The contraction of the secondary wind maximum and the formation of the moat are features of the binary vortex interaction. Concentric vorticity structure formation in binary vortex interaction requires a core vortex that is 4 to 6 times stronger than the outer vortex. The formation of concentric structures requires an outer vortex that is larger than the core vortex and with a separation distance that is within 6 times the core vortex radius. A core vortex with (without) a vorticity skirt allows the formation of an outer band at radii larger (smaller) than 3 times the core vortex radius. Moreover, the outer vortex for the formation of concentric structure is required to be at least 3 times larger than the core vortex radius for the core vortex with skirts. Our study also indicates that a strong tropical cyclone with a moat of 10 km to 20 km is able to organize a stirred field of vorticity with spatial scale of 40 km to 50 km into a concentric structure similar to those formed in the binary vortex interaction. Both the binary vortex interaction experiments and turbulent background vorticity experiments highlight the pivotal role of the core vorticity strength in maintaining itself, in stretching, organizing and stabilizing the outer vorticity field, and in shielding effect of the moat to prevent further merger and enstrophy cascade processes in concentric eyewall dynamics. Our results support the notion that concentric eyewalls form in strong tropical cyclones. In addition, our results give accounts to the satellite observations which indicate the formation of outer vorticity band at large or small radii away from the core. Our binary vortex interaction experiments also suggest that we need to observe the spatial and time characteristics of the vorticity field outside the core in the TC environment as well as the detailed core structure in order to better predict the formation of the concentric eyewalls.