The basic question underlying the work presented in this thesis concerns the self-organization and pattern formation in inanimate media when a fluid flow is present. This thesis studies the active and passive transport in turbulent and chaotic fluid flows. Thereby the focus is mainly of experimental nature. Especial interest is placed on the experimental observation and description of new patterns emerging, when active media is subjected to a turbulent fluid flow. In particular the effect of intense mixing as can be achieved by highly chaotic or turbulent fluid flows is to be uncovered. The first goal is to characterize and explain the phenomenon of a global reactive wave in a similar experimental realization observed by Fernandez Garca et al. in 2008. One step towards this goal is the measurement of the mixing caused by the Faraday experiment. This experiment consists in the vertical forcing of a container filled with liquid. Once the velocity field had been characterized we aimed for a definition of suitable analysis methods in order to study the transport of active media on different time and length-scales. Especially for intermediate range Damkoehler numbers, i.e. where the ratio of the timescale of the fluid flow and those of the reaction timescale is similar has not been studied in an experimental system with an excitable chemical reaction before. The analysis tools applied to this experimental model system might also partly be valid for the characterization of other reaction-diffusion-advection processes as found in many natural and men-made systems, such as plankton blooms in the ocean, chemicals in the atmosphere or bioreactors. The understanding of the role of the interplay of the typical timescales of the reaction and advection processes are to be discovered. A simple model accounting partly for some of the observed characteristics, such as the local scale-free transport, is formulated. The interplay of diffusive and advective processes is further studied in detail for a numerical model flow imitating the gulf-stream current. The details of this interplay can also lead to superdiffusion and scale-free transport.