Destabilization of the Symmetric Vortex and Formation of the Elliptical Eye of Typhoon Herb

Abstract

An elliptical eye was observed in Typhoon Herb during its passage around the Sakishima Islands located in the southwest of the Okinawa Islands in Japan on 30–31 July 1996. Later analysis showed that this elliptical eye had a structure with wavenumber 2 in the radar echo distribution, rainfall field, and pressure field. It is argued here that this structure is likely caused by a dynamic instability arising from radial shear in the tangential flow. To examine this possibility, a linear eigenvalue problem was set up using the asymmetric balance model in which the basic flow was based on the observed surface wind in Typhoon Herb, and the stability of the basic flow for both two- and three-dimensional perturbations was examined. Although for large Rossby numbers, the asymmetric balance model is not formally valid for higher azimuthal wavenumber perturbations, results certainly show that an unstable mode appears with the perturbation with wavenumber 2. In particular, the largest growth rate of the perturbation with wavenumber 2 is shown to occur for the three-dimensional perturbation. The eigenmode structure and rotation period of this three-dimensional perturbation with wavenumber 2 are comparable with the observations. These results suggest that barotropic instability due to the radial shear of tangential flow is relevant to the formation of the elliptical eye of Typhoon Herb.

Convectively Generated Potential Vorticity in Rainbands and Formation of the Secondary Eyewall in Hurricane Rita of 2005

“…This process, referred to as the eyewall replacement cycle (EWRC), can occur multiple times during a TC's life cycle (Willoughby et al 1982). Although concentric eyewalls and ERWCs are observed in some intense TCs (Black and Willoughby 1992;Oda et al 2005;Houze et al 2006Houze et al , 2007, not all major TCs develop these features. In this study, we will address why some intense TCs develop secondary eyewalls and others do not.…”

Spectral Analyses of the Polygonal Eye of Typhoon Sinlaku

“…The first one is that a ring-shaped high-voriticity region, which encloses a lower-vorticity core. The radial wind profile of Typhoon Herb (T9609) forming an elliptical eye implies such a vorticity distribution (Oda et al 2005). In this profile, perturbations with wavenumber m S 3 become unstable.…”

Optimal Excitation of Asymmetric Perturbations on an Axisymmetric Barotropic Vortex: A Linear Singular-Value Analysis

“…Indeed, the laboratory vortices produced by Kloosterziel and van Heijst (1991) have possessed a radial vorticity distribution similar to Sy ono's profile, and caused the wavenumber-2 instability. On the other hand, its existence in tropical cyclones is controversial, since, according to past observations of hurricanes and typhoons with elliptical eyes to date, it is certain that the vorticity minimum exists just outside of the positive vorticity core, but it is generally positive and at least zero (e.g., Oda et al 2005;Corbosiero et al 2006). Thus, further work is necessary for the application of Sy ono's profile to actual tropical cyclones.…”

“…Later, their second analysis was generalized to permit vertical variations in perturbations by adopting the quasigeostrophic potential vorticity equation instead of the nondivergent barotropic vorticity equation (Flierl 1988;Itano and Ishikawa 2002). On the other hand, Staley and Gall (1979) expanded the analysis to allow arbitrary wind profiles instead of the piecewise-constant vorticity profile, which triggered numerous stability analyses of a similar type based on observations (e.g., Oda et al 2005;Itano and Hosoya 2013) or theoretical interest (e.g., Gent and McWilliams 1986;Steffens 1988;Peng and Williams 1991).…”