The Algebraic Growth of Wavenumber One Disturbances in Hurricane-like Vortices

Abstract

Abstract An exact solution for the evolution of linearized perturbations of azimuthal wavenumber one on inviscid vortices was previously discovered for nondivergent vorticity dynamics on an f plane. The longtime asymptotics for this exact solution have been shown to allow an algebraic instability with unbounded growth even in the absence of exponentially growing modes. The necessary requirement for this instability is that there exist a local maximum in the basic-state angular velocity other than at the center of circulation. Hurricanes are naturally occurring examples of such vortices, due to the relatively calm eye and intense vorticity in the eyewall region. In this paper, the dynamics of this algebraic instability are studied in the context of the near-core dynamics of hurricanes. The longtime asymptotic solution can be written as a sum of three parts: a discrete mode whose amplitude grows in time as t1/2, an excitation of the neutral pseudomode (vortex displacement) that is constant in time, and resi...