Quasi-geostrophic three-dimensional flow in a cylinder

In this Letter a pseudo-spectral (collocation) method is used fur the probl em of inviscid. quasi-geostrophic flow in a cylinder of finite vertical ext ent. The numerical techniques employed are described. and results are prese nted for a variety of initial conditions. Previous work has indicated that in two dimensions relatively simple quasi-steady final states can be obtain ed [S. Li, D. Montgomery, Phys. Lett. A 218(1996) 281-291]. In this work we find similar long-time results. We also observe other long-lived states. i ncluding a tripole and a slowly precessing quadrupole, but these states eve ntually break down. These states tend to develop more quickly when the init ial vorticity varies with depth. It is found that, Tor example, the analogu e of a dipole in two dimensions consists of two blobs of potential vorticit y of opposite sign, roughly ellipsoidal in shape and elongated in the verti cal. The cross-sectional form of these final states is clearly related to t he fundamental linear Bessel modes of the system. as has been noted by prev ious authors. (C) 2000 Elsevier Science B.V. All rights reserved.