  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
travelling Rossby waves are superimposed. The associated Lagrangian motion is
studied with the aid of KAM (Kolmogorov--Arnold--Moser) 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
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.
