Studies of the wavenumber one instability in hurricane-like vortices

Smith and Rosenbluth (1990) showed that inviscid vortices that posess an angular velocity maximum other than at the center axis are susceptible to a wavenumber one instability whose amplitude grows as t^1/2. Such angular velocity profiles are typical for hurricanes due to their low-vorticity cores (the eye). In a recent presentation using non-divergent dynamics, Nolan and Montgomery (1999) demonstrated that this instability manifests itself as a growing wobble of the low-vorticity core, and that the growth rates in hurricane-like vortices are significant. The instability is caused by a resonance between a neutral mode in the vortex core (which represents a displacement of the low-vorticity eye) and vortex-Rossby waves which are trapped in the near-core region by the angular velocity maximum.

We present further analyses of the wavenumber one instability in hurricane-like vortices. In particular, we will show the impact of the instability when it reaches large amplitudes, leading to secondary instabilities in the near-core region of the vortex. These secondary instabilities ultimately cause enhanced mixing of high vorticity into the low vorticity core (even in absence of exponential instability), which has recently been hypothesized to be necessary for a storm to reach maximum potential intensity. We will also show the wavenumber one dynamics of hurricane-like vortices in more physical models such as the shallow-water primitive equations. The wavenumer one instability may provide a physical explanation for the commonly observed wobble in hurricane tracks, episodic occurrences of asymmetric convection in the near-core region, and the continuous mixing of high vorticity into the eye.