Chaotic transport and anomalous diffusion in a planar flow with a chain of vortices

Abstract

Chaotic transport in a time-periodic how with a chain of vortices bounded by two jet regions is numerically studied using the separatrix map. The stickiness of invariant surfaces in the jet regions produces long flights of tracer particles which leads to anomalous diffusion and the algebraic decay in the probability distributions for flight lengths. For a set of parameter values of the separatrix map explored, we found crossovers in the algebraic decay, which take place at time scales for a particle to penetrate the cantori leading to the large fluctuation of the algebraic exponents and the change in the nature of diffusion at various time scales. The relation between the exponents for flights and anomalous diffusion is discussed in connection with a continuous-time random walk model, and is compared with the results from numerical experiments.