A Study of Spiral Bands in a Linear Model of a Cyclonic Vortex

Abstract

This paper investigates the generation and propagation of spiral bands on an axisymmetric base-state vortex. A linear model is used to study the formation of bands from internal gravity-inertia waves in a barotropic atmosphere. Spiral bands form random perturbations placed on a vortex with unstable static stability that is equal for ascending and descending motion. This growing mode assumes the characteristics of pseudoadiabatic motion in a conditionally unstable atmosphere due to the coarse vertical resolution of the linear model. Implicit diffusion from the centered finite-difference scheme shifts the preferred growth modes from infinite wavenumbers, characteristic of inviscid analytical solutions, to 4?? and 4?r,ar wavelengths in numerical experiments. Here ?? and ?r are the angular and radial distances between grid points. Explicit diffusion representing subgrid-scale eddies shifts preferred modes to longer wavelengths. Rotation in the basic state is a necessary condition before the unstable gravity-inertia waves form spiral bands. Rotation also organizes stable perturbations into a banded pattern. Inertial instability and the Coriolis parameter are unimportant for band formation in these linear experiments. The distance between bands increases and the growth rate decreases in experiments in which adiabatic warming occurs with descent and warming due to latent heat release occurs with ascending motion.