Prototype geophysical vortex structures via large-scale statistical theory

Mark T. Dibattista, Andrew J. Majda, Bruce Turkington

Research output: Contribution to journalArticle

Abstract

Suitable vortex dipole pairs (modons) in eastward flow as well as monopole vortices in β-plane channel flow are characterized systematically in appropriate parameter regimes as the most-probable large-scale mean-field states predicted from a recent statistical theory (Turkington, 1998); this theory utilizes only a few conserved quantities involving energy, circulation, potential vorticity extrema, and the mean potential vorticity magnitude. The large-scale coherent structures emerge systematically from the statistical theory through maximization of a suitable coarse-grained entropy functional subject to the constraints imposed by these few conserved quantities. An accurate numerical procedure is developed here to study these states. For dilute PV theory, the most-probable large-scale coherent structures in eastward mean flows with nonzero β-effect are either dipolar vortex streets or zonal shear flows. The transition boundary of the predicted large-scale coherent structures between coherent vortices and zonal shear flows is related to a generalized Rhines' scale as the β-effect and energy are varied. The role of symmetry groups in the potential vorticity is emphasized here. In particular, in some parameter regimes the most-probable state within a given symmetry group of dipole pairs is not necessarily the most-probable large-scale coherent structure when the symmetry is broken.

Original languageEnglish (US)
Pages (from-to)235-283
Number of pages49
JournalGeophysical and Astrophysical Fluid Dynamics
Volume89
Issue number3-4
StatePublished - 1998

Fingerprint

vortex
Vortex flow
potential vorticity
Vorticity
prototypes
vortices
symmetry
zonal flow
shear flow
Shear flow
vorticity
vortex flow
channel flow
Channel flow
vortex streets
dipoles
entropy
energy
Entropy
range (extremes)

Keywords

  • Coherent structure
  • Dipole vortices
  • Eastward flow
  • Statistical theory

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Space and Planetary Science
  • Computational Mechanics
  • Mechanics of Materials
  • Astronomy and Astrophysics

Cite this

Prototype geophysical vortex structures via large-scale statistical theory. / Dibattista, Mark T.; Majda, Andrew J.; Turkington, Bruce.

In: Geophysical and Astrophysical Fluid Dynamics, Vol. 89, No. 3-4, 1998, p. 235-283.

Research output: Contribution to journalArticle

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