  Wave scattering phenomena are ubiquitous in almost all Sciences, from Biology
to Physics. Interestingly, it has been shown many times that different physical
systems are the stage to the same processes. The discoveries of such analogies
have resulted in a better understanding of Physics and are indications of the
universality of Nature. One stunning example is the observation that waves
propagating on a flowing fluid effectively experience the presence of a curved
space-time. In this thesis we will use this analogy to investigate, both
theoretically and experimentally, fundamental effects occurring around vortex
flows and rotating black holes. In particular, we will focus on light-bending,
superradiance scattering, and quasi-normal modes emission. The experimental
nature of this work will lead us to study these processes in the presence of
dispersive effects. Our results strengthen the link between vortices and
rotating black holes and open up new challenges to be addressed in the future.
