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Geophysical and Astrophysical Fluid Dynamics 2010, 115, iFirst
 

Summary: Geophysical and Astrophysical Fluid Dynamics
2010, 115, iFirst
Perturbed Rankine vortices in surface
quasi-geostrophic dynamics
B. J. HARVEY* and M. H. P. AMBAUM
Department of Meteorology, University of Reading, Reading RG6 6BB, UK
(Received 20 November 2009; in final form 11 February 2010)
An analytical dispersion relation is derived for linear perturbations to a Rankine vortex
governed by surface quasi-geostrophic dynamics. Such a Rankine vortex is a circular region of
uniform anomalous surface temperature evolving under quasi-geostrophic dynamics with
uniform interior potential vorticity. The dispersion relation is analysed in detail and compared
to the more familiar dispersion relation for a perturbed Rankine vortex governed by the Euler
equations. The results are successfully verified against numerical simulations of the full
equations. The dispersion relation is relevant to problems including wave propagation on
surface temperature fronts and the stability of vortices in quasi-geostrophic turbulence.
Keywords: Surface quasi-geostrophic dynamics; Vortices; Temperature fronts; Linear waves
1. Introduction
The simplest model for a two-dimensional (2-d) fluid is the familiar 2-d Euler equations
and there are many studies of vortices in this system. This note is concerned with
vortices in an alternative 2-d geophysical fluid model which has received renewed

  

Source: Ambaum, Maarten - Department of Meteorology, University of Reading

 

Collections: Geosciences