The dynamics of driven rotating flow in stadium-shaped domains

Abstract

Results are presented from an experimental investigation of the dynamics of driven rotating flows in stadium-shaped domains. The work was motivated by questions concerning the typicality of low-dimensional dynamical phenomena which are found in Taylor-Couette flow between rotating circular cylinders. In such a system, there is continuous azimuthal symmetry and travelling-wave solutions are found. In the present study, this symmetry is broken by replacing the stationary outer circular cylinder with one which has a stadium-shaped cross-section. Thus there is now only discrete symmetry in the azimuthal direction, and travelling waves are no longer observed. To begin with, the two-dimensional flow field was investigated using numerical techniques. This was followed by an experimental study of the dynamics of flow in systems with finite vertical extent. Configurations involving both right-circular and tapered inner cylinders were considered. Dynamics were observed which correspond to known mechanisms from the theory of finite-dimensional dynamical systems. However, flow behaviour was also observed which cannot be classified in this way. Thus it is concluded that while certain low-dimensional dynamical phenomena do persist with breaking of the continuous azimuthal symmetry embodied in the Taylor-Couette system, sufficient reduction of symmetry admits behaviour at moderately low Reynolds number which is without any low-dimensional characteristics.