Three-dimensional, Asymmetric, Nonhydrostatic, Unstable eigenmodes in Initially balanced, hurricane-like vortices

In recent years the asymmetric dynamics of tropical cyclones have been studied with a variety of simplified physical models, such as the two-dimensional Navier-Stokes equations, the shallow water equations, and the asymmetric balance formulation. We now extend this type of work into the fully nonhydrostatic, three-dimensional regime, by developing a linear stability analysis for three-dimensional, nonhydrostatic perturbations on an axisymmetric, balanced, hurricane-like vortex. The basic-state wind field and stratification are closely modelled after observations. While numerous earlier stability analyses have studied strictly two-dimensional (asymmetric) perturbations, or have assumed an exponential dependence in the vertical direction, we allow the eigenfunctions to vary in both the vertical and radial directions with harmonic dependence only in the azimuthal direction. This allows us to search for three-dimensional, baroclinic modes on the baroclinic vortex. Results indicate that the instability mechanism in the inner core is essentially that of the barotropic instability associated with the strong radial shear of the azimuthal winds in the eyewall.