Transport and mixing in traveling waves

An iterated map is constructed that captures the essential features of particle trajectories in a class of quasiperiodic traveling waves: large-amplitude single-frequency traveling waves with two-dimensional structure perturbed by a wave with a second frequency. The map provides an efficient method for numerical calculation of the transport and mixing properties of such waves, and is used here to study the properties of a chaotic separatrix layer. It is found that the average position increases linearly with time indicating the existence of a well-defined transport velocity. The transport velocity grows faster than linearly as the perturbation parameter k increases. The mixing takes the form of anomalous diffusion where the mean-square deviation of position grows as tν, with ν>1. The data is consistent with the diffusion exponent ν growing linearly with k.