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The Lagrangian dynamics of zonal jets in the atmosphere are considered, withparticular attention paid to explaining why, under commonly encounteredconditions, zonal jets serve as barriers to meridional transport. The velocityfield is assumed to be two-dimensional and incompressible, and composed of asteady zonal flow with an isolated maximum (a zonal jet) on which two or moretravelling Rossby waves are superimposed. The associated Lagrangian motion isstudied with the aid of KAM (Kolmogorov--Arnold--Moser) theory, includingnontrivial extensions of well-known results. These extensions includeapplicability of the theory when the usual statements of nondegeneracy areviolated, 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 anexplanation of the mechanism by which zonal jets serve as barriers tomeridional transport of passive tracers under commonly encountered conditions.Causes for the breakdown of such a barrier are discussed. It is argued that abarrier of this type accounts for the sharp boundary of the Antarctic ozonehole at the perimeter of the stratospheric polar vortex in the austral spring.Comment: Submitted to Journal of the Atmospheric Science

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