Vortex Interactions and Barotropic Aspects of Concentric Eyewall Formation

Abstract

Concentric eyewall formation can be idealized as the interaction of a tropical cyclone core with nearby weaker vorticity of various spatial scales. This paper considers barotropic aspects of concentric eyewall formation from modified Rankine vortices. In this framework, the following parameters are found to be important in concentric eyewall formation: vorticity strength ratio, separation distance, companion vortex size, and core vortex skirt parameter. A vorticity skirt on the core vortex affects the filamentation dynamics in two important ways. First, the vorticity skirt lengthens the filamentation time, and therefore slows moat formation in the region just outside the radius of maximum wind. Second, at large radii, a skirted core vortex induces higher strain rates than a corresponding Rankine vortex and is thus more capable of straining out the vorticity field far from the core. Calculations suggest that concentric structures result from binary interactions when the small vortex is at least 4-6 times as strong as the larger companion vortex. An additional requirement is that the separation distance between the edges of the two vortices be less than 6-7 times the smaller vortex radius. Broad moats form when the initial companion vortex is small, the vorticity skirt outside the radius of maximum wind is small, and the strength ratio is large. In concentric cases, an outer vorticity ring develops when the initial companion vortex is large, the vorticity skirt outside the radius of maximum wind is small, and the strength ratio is not too large. In general, when the companion vortex is 3 times as strong as the core vortex and the separation distance is 4-6 times the radius of the smaller vortex, a core vortex with a vorticity skirt produces concentric structures. In contrast, a Rankine vortex produces elastic interaction in this region of parameter space. Thus, a Rankine vortex of sufficient strength favors the formation of a concentric structure closer to the core vortex, while a skirted vortex of sufficient strength favors the formation of concentric structures farther from the core vortex. This may explain satellite microwave observations that suggest a wide range of radii for concentric eyewalls.

Western North Pacific Typhoons with Concentric Eyewalls

“…The maximum 1-min sustained wind speed was derived using the Dvorak T number. The microwave data are used to define the CE structure, the inner eyewall radius, Kallenbach 1997) and axisymmetrization of binary vortex interaction (Kuo et al 2004(Kuo et al , 2008. These dynamics highlight the importance of the strong core vortex.…”

“…Compared to the non-concentric eyewall typhoon composite, the concentric composite shows a relatively high intensity for a longer duration, rather than a rapid intensification process that can reach a higher intensity. Kuo et al (2004Kuo et al ( , 2008 hypothesized that axisymmetrization of positive vorticity perturbations around a strong and tight core of vorticity may lead to the formation of concentric eyewalls. The long duration of high intensity before secondary eyewall formation may provide a favorable environment for the axisymmetrization dynamics to operate.…”

“…The preponderance of large-radius CE in the western Pacific compared to other basins was further suggested by Hawkins et al (2006). Kuo et al (2008) discussed on the role vorticity skirts outside the TC core may play in the formation of CE structure of various sizes through the binary vortex interaction mechanism. Kossin and Sitkowski (2008) designed a new empirical model that will provide forecasters with a probability of 5 imminent CE formation.…”

Barotropic Aspects of Hurricane Structural and Intensity Variability

“…Kuo et al (2004) suggests the pivotal role of the vorticity strength of the core vortex in maintaining itself, and in strectching, organizing and stabilizing the outer vorticity field, and the shielding effect of the moat to prevent further merger and enstrophy cascade processes in concentric eyewall dynamics. Kuo et al (2008) further suggests that double eyewall of different sizes maybe explained by the binary vortex interaction with skirted parameter. The result also suggests that vorticity generation in the core and in the environment (via mesoscale convection) are of great importance in double eyewall dynamics.…”

“…The radar observation of typhoon Lekima (2001) near Taiwan (Kuo et al, 2004) indicates a huge area of convection outside the core vortex wraps around the inner eyewall to form concentric eyewalls in about 12 hours. Kuo et al (2008) also reported cases of passive microwave data that the formation of a concentric eyewall from organization of asymmetric convection outside the primary eyewall into a symmetric band that encircled the eyewalls. Two such concentric eyewalls examples are shown in Fig.…”