Editorial Type:
Article
Article Type:
Research Article

On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex

I. I. Rypina Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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M. G. Brown Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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F. J. Beron-Vera Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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H. Koçak Departments of Computer Science and Mathematics, University of Miami, Coral Gables, Florida

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M. J. Olascoaga Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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I. A. Udovydchenkov Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Print Publication:
01 Oct 2007
DOI:
https://doi.org/10.1175/JAS4036.1
Page(s):
3595–3610
Restricted access

Abstract

The Lagrangian dynamics of zonal jets in the atmosphere are considered, with particular attention paid to explaining why, under commonly encountered conditions, zonal jets serve as barriers to meridional transport. The velocity field is assumed to be two-dimensional and incompressible, and composed of a steady zonal flow with an isolated maximum (a zonal jet) on which two or more traveling Rossby waves are superimposed. The associated Lagrangian motion is studied with the aid of the Kolmogorov–Arnold–Moser (KAM) theory, including nontrivial extensions of well-known results. These extensions include applicability of the theory when the usual statements of nondegeneracy are violated, and applicability of the theory to multiply periodic systems, including the absence of Arnold diffusion in such systems. These results, together with numerical simulations based on a model system, provide an explanation of the mechanism by which zonal jets serve as barriers to the meridional transport of passive tracers under commonly encountered conditions. Causes for the breakdown of such a barrier are discussed. It is argued that a barrier of this type accounts for the sharp boundary of the Antarctic ozone hole at the perimeter of the stratospheric polar vortex in the austral spring.

Corresponding author address: I. I. Rypina, RSMAS/AMP, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. Email: irypina@rsmas.miami.edu

Abstract

The Lagrangian dynamics of zonal jets in the atmosphere are considered, with particular attention paid to explaining why, under commonly encountered conditions, zonal jets serve as barriers to meridional transport. The velocity field is assumed to be two-dimensional and incompressible, and composed of a steady zonal flow with an isolated maximum (a zonal jet) on which two or more traveling Rossby waves are superimposed. The associated Lagrangian motion is studied with the aid of the Kolmogorov–Arnold–Moser (KAM) theory, including nontrivial extensions of well-known results. These extensions include applicability of the theory when the usual statements of nondegeneracy are violated, and applicability of the theory to multiply periodic systems, including the absence of Arnold diffusion in such systems. These results, together with numerical simulations based on a model system, provide an explanation of the mechanism by which zonal jets serve as barriers to the meridional transport of passive tracers under commonly encountered conditions. Causes for the breakdown of such a barrier are discussed. It is argued that a barrier of this type accounts for the sharp boundary of the Antarctic ozone hole at the perimeter of the stratospheric polar vortex in the austral spring.

Corresponding author address: I. I. Rypina, RSMAS/AMP, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. Email: irypina@rsmas.miami.edu

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