Mixing by barotropic instability in a nonlinear model

A global, nonlinear, equivalent barotropic model is used to study the isentropic mixing of passive tracers by barotropic instability. Basic states are analytical zonal-mean jets representative of the zonal-mean flow in the upper stratosphere, where the observed 4-day wave is thought to be a result of barotropic, and possibly baroclinic, instability. As is known from previous studies, the phase speed and growth rate of the unstable waves is fairly sensitive to the shape of the zonal-mean jet; and the dominant wave mode at saturation is not necessarily the fastest growing mode; but the unstable modes share many features of the observed 4-day wave. Lagrangian trajectories computed from model winds are used to characterize the mixing by the flow. For profiles with both midlatitude and polar modes, mixing is stronger in midlatitude than inside the vortex; but there is little exchange of air across the vortex boundary. There is a minimum in the Lyapunov exponents of the flow and the particle dispersion at the jet maximum. For profiles with only polar unstable modes, there is weak mixing inside the vortex, no mixing outside the vortex, and no exchange of air across the vortex boundary. These results support the theoretical arguments that, whether wave disturbances are generated by local instability or propagate from other regions, the mixing properties of the total flow are determined by the locations of the wave critical lines and that strong gradients of potential vorticity are very resistant to mixing.