Chaotic Transport in Planar Periodic Vortical Flows

Abstract

We have studied a chaotic transport in a two-dimensional periodic vortical flow under a time-dependent perturbation with period T where the global diffusion occurs along the stochastic web. By using the Melnikov method we construct the separatrix map describing the approximate dynamics near the saddle separatrices. Focusing on the small T, the width of the stochastic layer is calculated analytically by using the residue criterion and the diffusion constant by using the random phase assumption and correlated random walks. The analytical results are in good agreements with the results of two different types of numerical simulations by integrations of the Hamilton's equation of motion and by iterations of the separatrix map, which establishes the validity of the use of the separatrix map.