Resonant flights and transient superdiffusion in a time-periodic, two-dimensional flow

Enhanced, passive transport is studied numerically in an oscillating vortex chain with stress-free boundary conditions. The long-range transport is found to be diffusive in the long-time limit with an effective diffusion coefficient D∗ that peaks dramatically in the vicinity of a few, well-defined resonant frequencies. Superdiffusive transients are also observed for frequencies near these resonant frequencies, with the duration of the transients diverging at the resonant frequencies. Standard analytical techniques based on the Melnikov approximation and on lobe dynamics fail to explain the behavior in the vicinity of these resonant peaks. An alternate explanation is provided, based on flights that have power-law scaling up to a maximum length that also diverges at the resonant frequencies. The long flights for frequencies near the resonant peaks occur because tracers in a lobe return (after an integer number of oscillation periods) to almost precisely the same location in the lobe of another vortex. These periodic orbits correspond to the formation — only at the resonant frequencies — of “tangle islands” within the chaotic region.