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.