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The structure of the separation bubble that appears in the secondary meridional flow between two coaxially rotating spheres at low and finite Reynolds number (Re) is considered. The low Re analytical study was motivated by recognizing some errors in the analytical work on this problem by Arunachalam and Majhi (1987, Q. Jl Mech. Appl. Math., 40, 47) whilst the finite Re experimental study was motivated by the desire to observe the separation bubble in the laboratory. Though the finite Re experiments were performed in a confined apparatus, they exhibit the qualitative features of the low Re theoretical predictions for the axisymmetric separation bubble that encloses two toroidal vortices symmetrically disposed above and below the mid‐plane of sphere separation, but strong effects of confinement are apparent. The flows observed include (i) a wall‐attached bubble symmetric about the mid‐plane at low Re, (ii) symmetric free‐standing bubbles at moderate Re, and (iii) an asymmetric bubble with flow separating from one sphere and attaching to the support shaft between the spheres at sufficiently high Re.

Flows in nature and technology are often associated with specific structures and pattern. This paper deals with the development and behaviour of such flow pattern. Flow structures are important for the mass, momentum and energy transport. The behaviour of different flow pattern is used by engineers to obtain an efficient mass and energy consumption. Mechanical power is transmitted via the momentum of rotating machine parts. Therefore the physical and mathematical knowledge of these basic concepts is important. Theoretical and experimental investigations of principle experiments are described in the following. We start with the classical problem of the flow between two concentric cylinders where the inner cylinder rotates. Periodic instabilities occur which are called Taylor vortices. The analogy between the cylindrical gap flow, the heat transfer in a horizontal fluid layer exposed to the gravity field and the boundary layer flow along concave boundaries concerning their stability behaviour is addressed. The vortex breakdown phenomenon in a cylinder with rotating cover is also described. A generalization to spherical sectors leads then to investigations with different boundary conditions. The spherical gap flow exhibits interesting phenomena concerning the nonlinear character of the Navier-Stokes equations. Multiple solutions in the nonlinear regime give rise to different routes during the laminar-turbulent transition. The interaction of two rotating spheres results in flow structures with separation and stagnation lines. Experimental results are confirmed by numerical simulations.

Shapes and structures of vortex breakdown phenomena in rotating fluids are visualized. We investigate the flow in a cylindrical container and in a cone between two spherical surfaces. The primary swirling flow is induced by the rotating upper disk in the cylindrical case and by the lower boundary in the spherical case. The upper surface can be fixed with a no slip condition or can be a stress-free surface. Depending on these boundary conditions and on the Reynolds number novel structures of recirculation zones are realized. Experiments are done to visualize the topological structure of the flow and to determine their existence range as function of the geometry and rotation rate. A comparison between the experimental and theoretical approach shows a good agreement in respect to the topological structures of the flows.

Rotating flow systems are often used to study stability phenomena and structure developments. The closed spherical gap problem is generalized into an open flow system by superimposing a mass flux in meridional direction. The basic solutions at low Reynolds numbers are described by analytical methods. The nonlinear supercritical solutions are simulated numerically and realized in experiments. Novel steady and time-dependent modes of flows are obtained. The extensive results concern the stability behaviour, non-uniqueness of supercritical solutions, symmetry behaviour and transitions between steady and time-dependent solutions. The experimental investigations concern the visualization of the various instabilities and the quatitative description of the flow structures including the laminar-turbulent transition. A comparison between theoretical and experimental results shows good agreement within the limit of rotational symmetric solutions from the theory.