Skip to content

Research at St Andrews

The stability and nonlinear evolution of quasi-geostrophic toroidal vortices

Research output: Contribution to journalArticle

DOI

Open Access permissions

Open

Abstract

We investigate the linear stability and nonlinear evolution of a three-dimensional toroidal vortex of uniform potential vorticity under the quasi-geostrophic approximation. The torus can undergo a primary instability leading to the formation of a circular array of vortices, whose radius is about the same as the major radius of the torus. This occurs for azimuthal instability mode numbers m ≥ 3, on sufficiently thin tori. The number of vortices corresponds to the azimuthal mode number of the most unstable mode growing on the torus. This value of m depends on the ratio of the torus’ major radius to its minor radius, with thin tori favouring high mode m values. The resulting array is stable when m = 4 and m = 5 and unstable when m = 3 and m ≥ 6. When m = 3 the array has barely formed before it collapses toward its centre with the ejection of filamentary debris. When m = 6 the vortices exhibit oscillatory staggering, and when m ≥ 7 they exhibit irregular staggering followed by substantial vortex migration, e.g. of one vortex to the centre when m = 7. We also investigate the effect of an additional vortex located at the centre of the torus. This vortex alters the stability properties of the torus as well as the stability properties of the circular vortex array formed from the primary toroidal instability. We show that a like-signed central vortex may stabilise a circular m-vortex array with m ≥ 6.
Close

Details

Original languageEnglish
Pages (from-to)60-78
JournalJournal of Fluid Mechanics
Volume863
Early online date22 Jan 2019
DOIs
Publication statusPublished - 25 Mar 2019

    Research areas

  • Quasi-geostrophic flows, Vortex instability

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. The merger of geophysical vortices at finite Rossby and Froude number

    Reinaud, J. N. & Dritschel, D. G., 10 Aug 2018, In : Journal of Fluid Mechanics. 848, p. 388-410

    Research output: Contribution to journalArticle

  2. Interaction between a quasi-geostrophic buoyancy filament and a heton

    Reinaud, J. N., Carton, X. & Dritschel, D. G., Sep 2017, In : Fluids. 2, 3, 20 p., 37.

    Research output: Contribution to journalArticle

  3. Interaction between a surface quasi-geostrophic buoyancy anomaly jet and internal vortices

    Reinaud, J. N., Dritschel, D. G. & Carton, X., Aug 2017, In : Physics of Fluids. 29, 8, 16 p., 086603.

    Research output: Contribution to journalArticle

  4. Homostrophic Vortex Interaction under External Strain in a Coupled QG-SQG Model

    Perrot, X., Reinaud, J. N., Carton, X. & Dritschel, D. G., 2010, In : Regul. Chaotic Dyn.. 15, 1, p. 66-83

    Research output: Contribution to journalArticle

Related by journal

  1. Journal of Fluid Mechanics (Journal)

    David Gerard Dritschel (Editor)
    2005 → …

    Activity: Publication peer-review and editorial work typesEditor of research journal

Related by journal

  1. On the regularity of the Green-Naghdi equations for a rotating shallow fluid layer

    Dritschel, D. G. & Jalali, M. R., 25 Apr 2019, In : Journal of Fluid Mechanics. 865, p. 100-136

    Research output: Contribution to journalArticle

  2. Scale-invariant singularity of the surface quasigeostrophic patch

    Scott, R. K. & Dritschel, D. G., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, 12 p., R2.

    Research output: Contribution to journalArticle

  3. Three-dimensional quasi-geostrophic vortex equilibria with m−fold symmetry

    Reinaud, J. N., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, p. 32-59

    Research output: Contribution to journalArticle

ID: 256888764