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dc.contributor.authorTsang, Yue-Kin
dc.contributor.authorDritschel, David G.
dc.identifier.citationTsang , Y-K & Dritschel , D G 2015 , ' Ellipsoidal vortices in rotating stratified fluids : beyond the quasi-geostrophic approximation ' , Journal of Fluid Mechanics , vol. 762 , pp. 196-231 .
dc.identifier.otherPURE: 161187157
dc.identifier.otherPURE UUID: 2f55ccc4-d31c-4094-81c7-c75fa531e043
dc.identifier.otherWOS: 000345575200010
dc.identifier.otherScopus: 85009455756
dc.identifier.otherWOS: 000345575200010
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697822
dc.descriptionSupport for this research has come from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).en
dc.description.abstractWe examine the basic properties and stability of isolated vortices having uniform potential vorticity (PV) in a non-hydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basic-state stratification for which both the Coriolis and buoyancy frequencies, f and N, are constant. Moreover, we take ƒ/N≪1, as typically observed in the Earth’s atmosphere and oceans. In the small Rossby number ‘quasi-geostrophic’ (QG) limit, when the flow is weak compared to the background rotation, there exist exact solutions for steadily rotating ellipsoidal volumes of uniform PV in an unbounded flow (Zhmur & Shchepetkin, Izv. Akad. Nauk SSSR Atmos. Ocean. Phys., vol. 27, 1991, pp. 492–503; Meacham, Dyn. Atmos. Oceans, vol. 16, 1992, pp. 189–223). Furthermore, a wide range of these solutions are stable as long as the horizontal and vertical aspect ratios λ and μ do not depart greatly from unity (Dritschel et al.,J. Fluid Mech., vol. 536, 2005, pp. 401–421). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, QG vortices are more stable than anticyclones at finite negative Rossby number, and generally less stable than cyclones at finite positive Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing μ. An unstable vortex often restabilises by developing a near-circular cross-section, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertia–gravity waves (IGWs) is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities, are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.rights© 2014. Cambridge University Press. This is a pre-copyedited, author-produced PDF of an article accepted for publication in Journal of Fluid Mechanics following peer review. The version of record Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation Tsang, Y-K. & Dritschel, D. G. Jan 2015 In : Journal of Fluid Mechanics. 762, p. 196-231 is available online at:
dc.subjectGeophysical and geological flowsen
dc.subjectRotating flowsen
dc.subjectVortex dynamicsen
dc.subjectWarm-core ringsen
dc.subjectGeophysical flowsen
dc.subjectOceanic vorticesen
dc.subjectQA Mathematicsen
dc.titleEllipsoidal vortices in rotating stratified fluids : beyond the quasi-geostrophic approximationen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Marine Alliance for Science & Technology Scotlanden
dc.contributor.institutionUniversity of St Andrews.Scottish Oceans Instituteen
dc.description.statusPeer revieweden

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