Lagrangian and Tracer Evolution in the Vicinity of an Unstable Jet

Abstract

The dynamics of Lagrangian particles and tracers in the vicinity of a baroclinically unstable zonal jet are investigated in a simple two-layer model with an initially quiescent lower layer. The presence of a growing wave induces a particle drift dominated by Stokes drift rather then the contribution of the wave to the mean Eulerian velocity. Stable and unstable waves have zonal Stokes drift with similar meridional structure while only unstable waves possess meridional drift, which is in the direction of increasing meridional wave displacement. Particle dispersion in the upper layer is maximum at critical lines, where the jet and phase speeds are equal. In the lower layer, dispersion is maximum where the wave amplitude is maximum. Zonal mean tracer evolution is formulated as an advection?diffusion equation with an order Rossby number advection and an order-one eddy diffusion. The latter is proportional to two-particle dispersion. Finite amplitude simulations of the flow reveal that small amplitude theory has predictive value beyond the range for which it is strictly valid. Mixing (as opposed to stirring) is maximum near cat?s-eye-like recirculation regions at the critical lines. In the lower layer the pattern of convergence and divergence of the flow locally increases tracer gradients, resulting in stirring yet with a much slower mixing rate than in the upper layer. Meridional eddy diffusion (or particle dispersion) alone is not sufficient for prediction of mixing intensity. Rotation, which is quantified by the cross-correlation of meridional and zonal displacements, must also be present for mixing. These results are consistent with observations of tracer and floats in the vicinity of the Gulf Stream.