Lobe transport analysis of the Kelvin-Stuart cat's eyes driven flow

Mixing and transport in the driven Kelvin-Stuart cat's eyes dynamical system is studied using lobe transport theory and the topological approximation method (TAM). The application of the TAM also provides a global bifurcation analysis. Lobe areas are calculated using the Melnikov amplitude function, which has been derived for the Kelvin-Stuart system. Results indicate that regions, originally in the exterior above the vortex chain, can be transported to the exterior below the vortex chain (and vice versa) by passing through the interior, and that a region within the interior of a given vortex can be transported to the interior of a neighboring vortex, or the interior of a vortex several vortices distant from the given vortex. Cumulative transport is shown to decrease with increasing perturbation frequency for a fixed value of perturbation strength. Cumulative transport increases with increasing perturbation strength for a fixed value of the structure index L. Cumulative transport approaches a characteristic maximum value for each set of parameter values. Results demonstrate a linear dependence of the maximum cumulative transport upon a universal flux function of the form proposed by Rom-Kedar and Poje, suggesting a possible scaling in the transport dependent on the structure index L.