Properties of chaotic advection in a 2-layer model of vortex flow

The transport properties of a two-dimensional, inviscid incompressible vortex flow using dynamical systems techniques are examined. The flow field induced by the interaction of a bottom topography with a background flow in a 2-layer fluid is considered. Using the concept of background currents, the dynamically consistent stream function of this flow is constructed. If the background flow is steady, then the trajectories of fluid particles coincide with streamlines. The flow field consists of a vortex region (VR) with closed streamlines bounded by a separatrix and a flowing region (FR) with streamlines going to infinity. In the presence of the oscillating perturbation the picture changes dramatically; fluid particles are entrained and detrained from the VR and chaotic particle motion occurs. We focus on how the change in frequency of the perturbation affects the transport and distribution of passive tracers. It's carried out experiment that allows us to estimate the number of fluid particles, initially uniformly filled whole vortex region, leaving the VR. The evolution particle number shows that when the perturbation frequency increases the mean transport decreases. However, the dependence of particle number leaved the VR on perturbation frequency is complicated. It has both global maximum and local extremums. The analyse of evolution Poincare map from the perturbation frequency showed that local extremums are related to the disappearance and overlap of resonance bands. It is suggested that the disappearance of resonance bands related to the limited of dependence of fluid particle travel time in the VR on the distance from tracer location to vortex center at absent of perturbation.