The flow in the gap between two concentric cylinders rotating relative to each other is known as Taylor-Couette (TC) flow. This topic is highlighted in understanding of much hydrodynamic instabilities. Depending on the rotation rate of the two cylinders, one can achieve either a linear stable regime (as in pipe flow) or an unstable regime (as in Rayleigh-Bénard convection). So, the Taylor-Couette-system represents for the Research Unit the link of the linear stability between the pipe- and the Rayleigh-Bénard-flows. Besides its relevance for a lot of applications in technology, the Taylor-Couette flow is also of fundamental interest in terms of transport properties in rotating systems, as Earth's atmosphere or accretion disks. A better understanding of the transport processes and the turbulent structures, a uniform description of these complex aspects - there are tasks of great importance for many domains.