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Quasi-geostrophic shallow-water doubly-connected vortex equilibria and their stability
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dc.contributor.author | Plotka, Hanna | |
dc.contributor.author | Dritschel, David Gerard | |
dc.date.accessioned | 2014-08-15T12:01:01Z | |
dc.date.available | 2014-08-15T12:01:01Z | |
dc.date.issued | 2013-05 | |
dc.identifier | 61437931 | |
dc.identifier | 4e371ec8-1ebc-4eb8-a435-cbe03b976a83 | |
dc.identifier | 000317659400003 | |
dc.identifier | 84876248766 | |
dc.identifier.citation | Plotka , 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 . https://doi.org/10.1017/jfm.2013.104 | en |
dc.identifier.issn | 0022-1120 | |
dc.identifier.other | ORCID: /0000-0001-6489-3395/work/64697834 | |
dc.identifier.uri | https://hdl.handle.net/10023/5172 | |
dc.description | H.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.abstract | We 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.format.extent | 29 | |
dc.format.extent | 11699993 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Fluid Mechanics | en |
dc.subject | Contour dynamics | en |
dc.subject | Rotating flows | en |
dc.subject | Vortex dynamics | en |
dc.subject | V-states | en |
dc.subject | 2-dimensional vortex | en |
dc.subject | Uniform vortices | en |
dc.subject | 2 dimensions | en |
dc.subject | Numerical algorithms | en |
dc.subject | Coherent structures | en |
dc.subject | Euler equations | en |
dc.subject | Merger | en |
dc.subject | Flows | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Quasi-geostrophic shallow-water doubly-connected vortex equilibria and their stability | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.contributor.institution | University of St Andrews. Marine Alliance for Science & Technology Scotland | en |
dc.contributor.institution | University of St Andrews. Scottish Oceans Institute | en |
dc.identifier.doi | https://doi.org/10.1017/jfm.2013.104 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/H001794/1 | en |
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