SEPARATRIX-MAP ANALYSIS OF CHAOTIC TRANSPORT IN PLANAR PERIODIC VORTICAL FLOWS

Abstract

We have studied 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 small T, the width of the stochastic layer is calculated analytically using the residue criterion and the diffusion constant is computed using the random phase assumption and the theory of correlated random walks. The analytical results are in good agreement with the results of two different types of numerical simulations: integrations of Hamilton's equation of motion and iterations of the separatrix map, which establishes the validity of the use of the separatrix map.