Cross-jet transport in quasi-geostrophic simulations

Cross-jet transport of passive tracers, and in particular the extent to which jets indicate the presence of barriers to mixing, is a matter of considerable current interest in studies of extratropical jets in the upper troposphere and upper oceans. Turbulent jets are immersed in an active eddy field, and transport is significantly influenced by details of the eddy field. Using QG beta-plane models to study meridional transport across zonally oriented jets, we find important roles played by both the large-scale eddy field, and by Rossby waves travelling along the potential vorticity gradients organized by this eddy field. Our results include an illustration of the differing effects produced by large scale eddy fields in "externally stirred" barotropic models and "internally stirred" baroclinic models. Each kind of model has been given attention in attempts to account for jet formation. The baroclinic results statistically complement several recent studies using kinematic models of mixing across zonal jets with imposed eddy fields. The barotropic results suggest a limit to the utility of small scale stirring models in understanding meridional transport, except perhaps by way of contrast.

Baroclinic simulations indicate existence a scaling regime, for tracers released outside pro-grade jets, intermediate between the early "ballistic" regime and the ultimate "normal diffusion" regimes familiar from the Taylor analysis. The ballistic regime ends when the large eddies first sweep tracers into the core regions of westerly jets. The sweeping time-scale is an important one in meridional transport, and can be related to the scale and energy levels of the large-scale eddies. In the intermediate regime, tracers are swept into and later out of the narrow westerly jets by the large-scale eddies, sometimes being entrained for long times in the jets before being cast to one side or the other in wave-breaking events. Rms meridional displacement during this period scales with time to a clearly defined power less than one-half: the exponent effectively provides a statistical summary of previous kinematic mixing models. The anomalous regime ends when enough tracers have made it across the jet nearest to the latitude of release. Both the scaling exponent and the regime length, which are related in a way only qualitatively understood, reflect the frequency of wave-breaking. Although the physics at the pv gradients is different, the transport is qualitatively analogous to transport through an array of vortices, for which sub-diffusive scaling has also been observed.

Transport in barotropic simulations is qualitatively different. Unlike the result in the baroclinic case, tracers released far from jets leave the ballistic regime long before, on statistical average, particles have reached the cores of westerly jets. A recent argument argument relating jet scale to the end of the ballistic regime, proposed on the basis of results from spin-down experiments using a barotropic model, thus seems to be inappropriate for forced dissipative barotropic simulations. The period of sub-diffusive spreading is far longer than in the baroclinic case, and must be regarded as unrealistic as the level of variability seen in the jets themselves. An argument relating jet scale to the end of the ballistic regime, recently proposed on the basis of results from spin-down experiments using a barotropic model, thus seems to be inappropriate for forced dissipative barotropic simulations.