Polygonal eye-walls in barotropic, hurricane-like vortices

An analytical and numerical study on the existence and maintenance of polygonal vorticity features in the core of a barotropic, hurricane-like vortex has been carried out. For the numerical experiments, linear and non-linear versions of a non-divergent, semispectral barotropic numerical model, formulated in a cylindrical coordinate system moving with the vortex on an f- and beta-plane, were used. Analytical solutions were obtained using the barotropic vorticity equation on an f-plane.

The study shows that in the absence of atmospheric diffusion or in cases of weak atmospheric diffusion, which is possibly a realistic assumption in real tropical cyclones above the boundary layer, time-persistent polygonal patterns of relative vorticity develop in the vortex core. The polygonal vorticity features occur in cycles and are manifestations of secondary vortices to the original symmetric vortex that are purely advected about the vortex centre by the mean swirling flow. At the end of each cycle, the relative vorticity distribution becomes symmetric again. The existence of a rotating vortex asymmetry of azimuthal wave number one leads to erratic or cycloidal motion of the vortex in question. This may have strong implications for the operational track prediction of tropical cyclones in the cases where polygonal eye-walls are observed.

The results obtained with the analytical model and the linear and nonlinear numerical calculations agree very well with observations of polygonal eye-walls of convection in real tropical cyclones: both the results of the present study and the observations show that most polygonal features rotate cyclonically about the vortex centre; they are located usually in the immediate vicinity of the radius of maximum tangential wind speed, which approximately represents the centre of the eye-wall region in a real tropical cyclone; their speed of rotation corresponds approximately with the symmetric tangential wind speed in the eye-wall region; their period of existence ranges from about ten minutes to several hours; they occur in cycles, interrupted by periods of symmetric eye-walls or polygonal eye-walls of a different wave number; and finally, they are associated with looping or erratic motion. The agreement of the analytical and numerical results of the present study with the observations suggest a simple and fundamental dynamical mechanism for the development and maintenance of polygonal eye-walls in tropical cyclones.