### 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 language | English (US) |
---|---|

Pages (from-to) | 235-283 |

Number of pages | 49 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 89 |

Issue number | 3-4 |

State | Published - 1998 |

### Fingerprint

### 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

*Geophysical and Astrophysical Fluid Dynamics*,

*89*(3-4), 235-283.

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

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 89, no. 3-4, pp. 235-283.

}

TY - JOUR

T1 - Prototype geophysical vortex structures via large-scale statistical theory

AU - Dibattista, Mark T.

AU - Majda, Andrew J.

AU - Turkington, Bruce

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - Coherent structure

KW - Dipole vortices

KW - Eastward flow

KW - Statistical theory

UR - http://www.scopus.com/inward/record.url?scp=0033500129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033500129&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033500129

VL - 89

SP - 235

EP - 283

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 3-4

ER -