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dc.contributor.authorPłotka, H.
dc.contributor.authorDritschel, D.G.
dc.identifier.citationPłotka , H & Dritschel , D G 2011 , ' Shallow-water vortex equilibria and their stability ' , Journal of Physics: Conference Series , vol. 318 , no. Section 6 , 062019 .
dc.identifier.otherPURE: 117826100
dc.identifier.otherPURE UUID: 54e18963-aff1-4af9-b32d-0333b798bfb4
dc.identifier.otherScopus: 84856344196
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697727
dc.description.abstractWe first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, L = c/f where c = √gH is a characteristic gravity-wave speed, g is gravity (or "reduced" gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call "quasi-equilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
dc.relation.ispartofJournal of Physics: Conference Seriesen
dc.rights© 2012 Plotka et al. This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 3.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited.en
dc.subjectQA Mathematicsen
dc.titleShallow-water vortex equilibria and their stabilityen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. University of St Andrewsen
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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