### 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) |
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Pages (from-to) | 235-283 |

Number of pages | 49 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 89 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1998 |

### Keywords

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

### ASJC Scopus subject areas

- Computational Mechanics
- Astronomy and Astrophysics
- Geophysics
- Mechanics of Materials
- Geochemistry and Petrology

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## Cite this

*Geophysical and Astrophysical Fluid Dynamics*,

*89*(3-4), 235-283. https://doi.org/10.1080/03091929808203687