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, described and visualized a non-attracting invariant chaotic set defining chaotic scattering, fractality, and trapping of incoming particles. Geometry and topology of chaotic scattering have been studied and visualized. 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. Mixing, trapping, and fractal properties of passive particles have been studied under the influence of a white noise with different amplitudes and frequency ranges. A new effect of clustering the particles in a noised flow has been demonstrated in numerical experiments.

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