# Quasi-geostrophic three-dimensional flow in a cylinder

## Author

**C. Macaskill**

## Status

Research Report 98-32

Date: 11 December 1998

## Abstract

In this paper a pseudo-spectral (collocation) method is used for the
problem of inviscid, quasi-geostrophic flow in a cylinder of finite
vertical extent. The numerical techniques employed are described, and
results are presented for a variety of initial conditions. Previous
work has indicated that in two dimensions relatively simple
quasi-steady final states can be obtained (S. Li and D. Montgomery,
Phys. Lett. A, 218, pp 281-291, 1996). In this work we find similar
long-time results. We also observe other long-lived states, including
a tripole and a slowly precessing quadrupole, but these states
eventually break down. These states tend to develop more quickly when
the initial vorticity varies with depth. It is found that, for
example, the analogue of a dipole in two dimensions consists of two
blobs of potential vorticity of opposite sign, roughly ellipsoidal in
shape and elongated in the vertical. The cross-sectional form of these
final states is clearly related to the fundamental linear Bessel modes
of the system, as has been noted by previous authors.

## Key phrases

potential vorticity. quasi-geostrophy. rotating, stratified flow. cylindrical flow.

## AMS Subject Classification (1991)

Primary: 76M

Secondary: 76C05,76U05,76V05

## Content

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Sydney Mathematics and Statistics