Isothermal spherical Couette flow

Abstract

We summarise different types of instabilities and flow patterns in isothermal spherical Couette flows as a function of the aspect ratio. The flow of a viscous incompressible fluid in the gap between two concentric spheres was investigated for the case, that only the inner sphere rotates and the outer one is stationary. Flow visualisation studies were carried out for a wide range of Reynolds numbers and aspect ratios to determine the instabilities during the laminar-turbulent transition and the corresponding critical Reynolds numbers as a function of the aspect ratio. It was found, that the laminar basic flow loses its stability at the stability threshold in different ways. The instabilities occurring depend strongly on the aspect ratio and the initial conditions. For small and medium aspect ratios (β ≤ 0.25), experiments were carried out as a function of Reynolds number to determine the regions of existence for basic flow, Taylor vortex flow, supercritical basic flow. For wide gaps, however, Taylor vortices could not be detected by quasistationary increase of the Reynolds number. The first instability manifests itself as a break of the spatial symmetry and non-axisymmetric secondary waves with spiral arms appear depending on the Reynolds number. For β = 0.33, spiral waves with an azimuthal wave number m = 6, 5and 4 were found, while in the gap with an aspect ratio of β = 0.5spiral waves with m = 5, 4 and 3 spiral arms exist. For β = 1.0, we could detect spiral waves with m = 4, 3 and 2 arms. We compare the experimental results for the critical Reynolds numbers and wave numbers with those obtained by numerical calculations. The flow modes occurring at the poles look very similar to those found in the flow between two rotating disks. Effects of non-uniqueness and hysteresis are observed in this regime.