Quasi-geostrophic three-dimensional flow in a cylinder


C. Macaskill


Research Report 98-32
Date: 11 December 1998


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


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Sydney Mathematics and Statistics