The Wavenumber-One Instability and Trochoidal Motion of Hurricane-like Vortices

In a previous paper, the authors discussed the dynamics of an instability that occurs in inviscid, axisymmetric, two-dimensional vortices possessing a low-vorticity core surrounded by a high-vorticity annulus. Hurricanes, with their low-vorticity cores (the eye of the storm), are naturally occurring examples of such vortices. The instability is for asymmetric perturbations of azimuthal wavenumber-one about the vortex, and grows in amplitude as t 1/2 for long times, despite the fact that there can be no exponentially growing wavenumber-one instabilities in inviscid, two-dimensional vortices. This instability is further studied in three fluid flow models: with highresolution numerical simulations of two-dimensional flow, for linearized perturbations in an equivalent shallowwater vortex, and in a three-dimensional, baroclinic, hurricane-like vortex simulated with a high-resolution mesoscale numerical model.