Nonlinear fractal dynamics and clustering of passive particles by a hydrodynamic vortex and a current

We investigate typical mixing and fractal properties of chaotic scattering of passive particles in open hydrodynamic flows taking as an example a model two-dimensional incompressible flow composed of a fixed point vortex and a background current with a periodic component, the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere. We have found and described a non-attracting invariant chaotic set defining chaotic scattering and trapping of incoming particles. Geometry and topology of chaotic scattering have been studied. Scattering functions in the mixing zone have been found to have a fractal structure with a complicated hierarchy that has been described in terms of strophes and epistrophes. A new effect of clustering has been demonstrated in numerical experiments. Mixing, trapping, and fractal properties of passive particles have been studied under the influence of a white noise with different amplitudes and frequency ranges. Using the results obtained, we have known how to control these properties of open hydrodynamic flows varying control parameters.