Polygonal Eyewalls, Asymmetric Eye Contraction, and Potential Vorticity Mixing in Hurricanes

Abstract

Hurricane eyewalls are often observed to be nearly circular structures, but they are occasionally observed to take on distinctly polygonal shapes. The shapes range from triangles to hexagons and, while they are often incomplete, straight line segments can be identified. Other observations implicate the existence of intense mesovortices within or near the eye region. Is there a relation between polygonal eyewalls and hurricane mesovortices? Are these phenomena just curiosities of the hurricane's inner-core circulation, or are they snapshots of an intrinsic mixing process within or near the eye that serves to determine the circulation and thermal structure of the eye? As a first step toward understanding the asymmetric vorticity dynamics of the hurricane's eye and eyewall region, these issues are examined within the framework of an unforced barotropic nondivergent model. Polygonal eyewalls are shown to form as a result of barotropic instability near the radius of maximum winds. After reviewing linear theory, simulations with a high-resolution pseudospectral numerical model are presented to follow the instabilities into their nonlinear regime. When the instabilities grow to finite amplitude, the vorticity of the eyewall region pools into discrete areas, creating the appearance of polygonal eyewalls. The circulations associated with these pools of vorticity suggest a connection to hurricane mesovortices. At later times the vorticity is ultimately rearranged into a nearly monopolar circular vortex. While the evolution of the finescale vorticity field is sensitive to the initial condition, the macroscopic end-states are found to be similar. In fact, the gross characteristics of the numerically simulated end-states are predicted analytically using a generalization of the minimum enstrophy hypothesis. In an effort to remove some of the weaknesses of the minimum enstrophy approach, a maximum entropy argument developed previously for rectilinear shear flows is extended to the vortex problem, and end-state solutions in the limiting case of tertiary mixing are obtained. Implications of these ideas for real hurricanes are discussed.

Polygonal Eyewall and Mesovortices Structure in a Numerically Simulated Typhoon Rusa

“…The radial outflow that was modified by the mesovortices transported the high e air from the eye into the eyewall, and consequently the convective activities in the eyewall were enhanced there. The horizontal distribution of the PV showed the wave-like pattern near the eyewall, which was quite similar to the ideal numerical experiments of Schubert et al (1999) and Kossin and Schubert (2001).…”

“…After t=53h30m, the positive PV anomalies collapsed in the westward side, and the PV increased inside of the eyewall. These results are quite similar to Schubert et al (1999) and Kossin and Schubert (2001). They indicated that the reversal of the radial PV gradient near the eyewall set the stage for dynamic instability and rearrangement of the PV distribution in the barotropic model.…”

“…Kuo et al (1999) attributed the elliptical eye of Typhoon Herb (1996) to a wavenumber-2 vortex Rossby wave that propagated upwind azimuthally near the eyewall. Schubert et al (1999) suggested that the polygonal eyewall and mesovortices in hurricanes formed as a result of barotropic instability near the radius of maximum winds, around which the potential vorticity maximum was found. Kossin and Schubert (2001) extended this work, and they suggested that a variety of polygonal shapes showed up due to the merge of the mesovortices around the eyewall and that this process was essential for a hurricane's rapid intensification.…”

Tropical‐cyclone intensification and predictability in three dimensions

“…Complete breakdown of the eyewall is not observed, however (cf. Schubert et al, 1999). The evolution is consistent with the picture of propagating near-discrete and sheared vortex Rossby waves and localized mixing events between the eyewall and its interior and exterior.…”

Intensity forecast experiment of hurricane Rita (2005) with a cloud‐resolving, coupled hurricane–ocean modelling system

“…Weaker secondary circulation and convergence at low level is less conducive to tempering the shear instability associated with the vorticity ring (Nolan, 2001;Montgomery et al, 2002). As a result, redistribution of vorticity along the radial direction could be expected (Schubert et al, 1999;Kossin and Schubert, 2001) and the radial profile of vorticity outside the eyewall was broadened (see black solid line in Figure 6). According to the beta-skirt axisymmetrization hypothesis Figure 6.…”