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

Abstract

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 t1/2 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 high-resolution numerical simulations of two-dimensional flow, for linearized perturbations in an equivalent shallow-water vortex, and in a three-dimensional, baroclinic, hurricane-like vortex simulated with a high-resolution mesoscale numerical model. The instability is found to be robust in all of these physical models. Interestingly, the algebraic instability becomes an exponential instability in the shallow-water vortex, though the structures of the algebraic and exponential modes are nearly identical. In the three-dimensional baroclinic vortex, the instability quickly leads to substantial inner-core vorticity redistribution and mixing. The instability is associated with a displacement of the vortex center (as defined by either minimum pressure or streamfunction) that rotates around the vortex core, and thus offers a physical mechanism for the persistent, small-amplitude trochoidal wobble often observed in hurricane tracks. The instability also indicates that inner-core vorticity mixing will always occur in such vortices, even when the more familiar higher-wavenumber barotropic instabilities are not supported.