Transition of free-surface flow modes in Taylor-Couette system

This paper presents our numerical and experimental results of the bifurcation found in Taylor-Couette system with a free surface. The lengths of the two concentric cylinders are finite and their axes are parallel to the direction of the gravitational force. When the end walls of the cylinders are fixed and stationary, numerical and experimental studies have shown that the flow has multiple patterns depending on the cylinder lengths and the Reynolds numbers. Experimental studies on flows with free surfaces also gave various flow modes. Our result shows that the measured and predicted time-dependent displacements of the free surface are in favorable agreement. In case of the cylinder length comparable with the gap width between the cylinders, gradual accelerations of the inner cylinder bring the normal mode flows with one, three and five toroidal vortices. The exchanges of stabilities between these flow modes are summarized in a phase diagram.