Numerical study of flows in a cylindrical container with rotating bottom and top flat free surface

Numerical study was conducted for steady swirling flows of viscous incompressible fluid confined in cylindrical containers driven by the bottom wall rotating at constant angular velocity with top free surface. The flow axisymmetry and the free-slip boundary condition is assumed at the top flat surface of the cylinder. Parametric computation was performed over a wide range of the Reynolds number Re and the radius to height aspect ratio h which covers parameter range not previously studied. Steady solutions disclosed a variety of flow patterns which include corner and surface bubbles with inner structures not noticed in the previous studies. Associated parameter regions are mapped on the parameter plane (h, Re) as a flow state diagram. It is shown that the bifurcation diagram is more complicated than previously believed. Comparison with the previous experimental and numerical studies is discussed in detail.