Skip to content

Research at St Andrews

A balanced approach to modelling rotating stably stratified geophysical flows

Research output: Contribution to journalArticle

Author(s)

David Gerard Dritschel, Alvaro Viúdez

School/Research organisations

Abstract

We describe a new approach to modelling three-dimensional rotating stratified flows under the Boussinesq approximation. This approach is based on the explicit conservation of potential vorticity, and exploits the underlying leading-order geostrophic and hydrostratic balances inherent in these equations in the limit of small Froude and Rossby numbers. These balances are not imposed, but instead are used to motivate the use of a pair of new variables expressing the departure from geostrophic and hydrostratic balance. These new variables are the ageostrophic horizontal vorticity components, i.e. the vorticity not directly associated with the displacement of isopycnal surfaces. The use of potential vorticity and ageostrophic horizontal vorticity, rather than the usual primitive variables of velocity and density, reveals a deep mathematical structure and appears to have advantages numerically. This change of variables results in a diagnostic equation, of Monge-Amp re type, for one component of a vector potential phi, and two Poisson equations for the other two components. The curl of phi gives the velocity field while the divergence of phi is proportional to the displacement of isopycnal surfaces. This diagnostic equation makes transparent the conditions for both static and inertial stability, and may change form from (spatially) elliptic to (spatially) hyperbolic even when the flow is statically and inertially stable. A numerical method based on these new variables is developed and used to examine the instability of a horizontal elliptical shear zone (modelling a jet streak). The basic-state flow is in exact geostrophic and hydrostratic balance. Given a small perturbation however, the shear zone destabilizes by rolling up into a street of vortices and radiating inertia-gravity waves.

Close

Details

Original languageEnglish
Pages (from-to)123-150
Number of pages28
JournalJournal of Fluid Mechanics
Volume488
DOIs
Publication statusPublished - 10 Aug 2003

    Research areas

  • Potential-vorticity, 2-Dimensional Flows, Gravity-waves, Turbulence, Dynamics, Surgery

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. 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

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

ID: 253248