Inertia-Buoyancy Waves in Hurricanes

Abstract

This study is an attempt to model spiral rainbands in hurricanes as inertia-buoyancy waves. The model is based on the nonhydrostatic equations that describe, in cylindrical coordinates, linear perturbations on a barotropic vortex imbedded in a uniformly stratified atmosphere. Solutions are obtained by the assumption of imaginary exponential variation in all coordinates except radius algebraic elimination of all the dependent variables except geopotential, and numerical integration to obtain the radial structure. This system supports waves whose frequencies are confined to a passband between the local inertia frequency and the buoyancy frequency and which obtain energy at the expense of the mean flow's kinetic energy by the mechanism proposed by Kurihara (1976). All waves subject to this instability propagate wave energy from low values of their Doppler-shifted frequency toward high values and sustain an eddy flux of angular momentum out of the vortex center. Although the instability may double or triple the wave energy flux, it is not strong enough to explain the formation of outward propagating waves because of geometric spreading of the wave energy. In the eye wall the local inertia frequency is less than an hour, so the minimum possible frequency for the simulated waves excited there is higher than that observed for spiral rainbands in nature. The differential equation governing the wave's radial structure becomes singular when the frequency is Doppler-shifted to the buoyancy frequency, resulting in the absorption of the wave by a process analogous to that occurring at critical levels for vertically propagating buoyancy waves.