Stability, transition and turbulence in rotating cavities

This chapter reviews striking features of boundary-layer instabilities induced by different mechanisms and related to transition to turbulence in rotating flows with walls. Besides its fundamental importance as a three-dimensional prototype flow, confined flow between rotating discs has been extensively examined because of its relevance to many industrial applications such as turbomachinery and engineering processes. Many studies using stability analyses and experiments have been devoted to the onset of unstable waves and to the mechanisms associated with them. Here, we focus on how numerical investigations may provide insights and complement experimental data and analytical results by providing the full velocity field in well-controlled flows within idealized configurations. Rotor-stator and rotating cavity with radial throughflow are investigated. At a critical rotation rate, axisymmetric and/or three-dimensional structures appear in the Bödewadt and Ekman layers. All features of the transitions in these rotating cavities are documented. A comparison of the wave numbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both Type II (or A) and Type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.