Dynamics of flow structures and surface shapes in the surface switching of rotating fluid

Abstract

We present a study of the dynamics of the free-surface shape of a flow in a cylinder driven by a rotating bottom. Near the critical Reynolds number of the laminar–turbulent transition of the boundary layer, the free surface exhibits irregular surface switching between axisymmetric and non-axisymmetric shapes, and the switching often occurs with a significant change in the free-surface height. Although such surface deformation is known to be caused by the flow structures, the detailed flow structures of a rotating fluid with a large surface deformation have yet to be analysed. We thus investigate the velocity distribution and surface shape dynamics and show that the flow field during the loss of its axisymmetry is similar to that predicted by the theory of Tophøj et al. (Phys. Rev. Lett., vol. 110, 2013, 194502). The slight difference observed by quantitative comparison is caused by the fact that the basic flow of our study contains a weak rigid-body rotation in addition to the potential flow assumed by the theory. Furthermore, the observed non-axisymmetric surface shape, which has an elliptic horizontal cross-section, is generally associated with a quadrupole vortex structure. It is also found that the relative position between the free surface and the flow structure changes before and after the detachment of the free surface from the bottom. The change just after the detachment is drastic and occurs via a transient dipole-like vortex structure.