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dc.contributor.authorPlotka, Hanna
dc.contributor.authorDritschel, David Gerard
dc.identifier.citationPlotka , H & Dritschel , D G 2013 , ' Quasi-geostrophic shallow-water doubly-connected vortex equilibria and their stability ' , Journal of Fluid Mechanics , vol. 723 , pp. 40-68 .
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697834
dc.descriptionH.P. acknowledges the support of a NERC studentship. D.G.D. received support for this research from the UK Engineering and Physical Sciences Research Council (grant EP/H001794/1).en
dc.description.abstractWe examine the form, properties, stability and evolution of doubly-connected (two-vortex) relative equilibria in the single-layer ƒ-plane quasi-geostrophic shallow-water model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio γ =L/LD between the horizontal size of the vortices and the Rossby deformation length; the area ratio α of the smaller to the larger vortex; and the minimum distance δ between the two vortices. We vary 0 < γ ≤ 10 and 0.1 ≤ α ≤ 1.0, determining the boundary of stability δ = δC(γ,α). We also examine the nonlinear development of the instabilities and the transitions to other near-equilibrium configurations. Two modes of instability occur when δ < δC: a small -γ asymmetric (wave 3) mode, which is absent for α ≳ 0.6; and a large -γ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near δC may be classified as follows: (i) vacillations about equilibrium for γ ≳ 2.5; (ii) partial straining out, associated with the small -γ mode, where either one or both of the vortices get smaller for γ ≲ 2.5 and α ≲ 0.6; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the large-γ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.subjectContour dynamicsen
dc.subjectRotating flowsen
dc.subjectVortex dynamicsen
dc.subject2-dimensional vortexen
dc.subjectUniform vorticesen
dc.subject2 dimensionsen
dc.subjectNumerical algorithmsen
dc.subjectCoherent structuresen
dc.subjectEuler equationsen
dc.subjectQA Mathematicsen
dc.titleQuasi-geostrophic shallow-water doubly-connected vortex equilibria and their stabilityen
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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