Skip to content

Research at St Andrews

Simply-connected vortex-patch shallow-water quasi-equilibria

Research output: Contribution to journalArticle

DOI

Open Access permissions

Open

Abstract

We examine the form, properties, stability and evolution of simply-connected vortex-patch relative quasi-equilibria in the single-layer ƒ-plane shallow-water model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasi-equilibria. Namely, these are the ratio γ=L/LD between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio λ between the minor to major axes of the vortex; and a potential vorticity (PV)-based Rossby number Ro=q′/ƒ, the ratio of the PV anomaly q′ within the vortex to the Coriolis frequency ƒ. By defining an appropriate steadiness parameter, we find that the quasi-equilibria remain steady for long times, enabling us to determine the boundary of stability λc=λc(γ, Ro), for 0.25≤γ≤6 and |Ro|≤1. By calling two states which share γ,|Ro| and λ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic (Ro>0) and anticyclonic (Ro<0) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for large-γ, large-Ro states, (b) filamentation for small-γ states and (c) vortex splitting, asymmetric for intermediate-γ and symmetric for large-γ states.

Close

Details

Original languageEnglish
Pages (from-to)481-502
Number of pages22
JournalJournal of Fluid Mechanics
Volume743
Early online date5 Mar 2014
DOIs
Publication statusPublished - 5 Mar 2014

    Research areas

  • Rotating flows , Shallow water flows, Vortex dynamics

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

View graph of relations

Related by author

  1. Comparison of the Moist Parcel-In-Cell (MPIC) model with large-eddy simulation for an idealized cloud

    Böing, S. J., Dritschel, D. G., Parker, D. J. & Blyth, A. M., 29 Apr 2019, In : Quarterly Journal of the Royal Meteorological Society. In press, 17 p.

    Research output: Contribution to journalArticle

  2. 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

  3. 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

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. The stability and nonlinear evolution of quasi-geostrophic toroidal vortices

    Reinaud, J. N. & Dritschel, D. G., 25 Mar 2019, In : Journal of Fluid Mechanics. 863, p. 60-78

    Research output: Contribution to journalArticle

  4. 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: 101380536