Mode formation of free surface rotating flow between concentric vertical cylinders

Mode exchanges of flows between concentric and rotating cylinders with vertical axes have been studied by numerical and experimental approaches. The lengths of the cylinders are finite, and the inner cylinder rotates and the outer cylinder is stationary. The bottom end wall of the annulus is a fixed solid wall and the top is a free surface between a working liquid and the air, and the wall condition is axially asymmetric. This gives one of the modifications of Taylor-Couette system. In this system, the normal mode flow has an inward flow on the lower end wall and an outward flow near the free surface. In experiment, visualized flows are observed from the top and the side of the cylinders, and the position of the free surface is measured. Numerical methods are based on the unsteady axisymmetric equations, and the gravitational acceleration and the surface tension are considered to formulate the dynamics of the free surface. The experimental result and numerical result show the primary mode, the secondary normal mode and the anomalous mode, which are similar to the modes found in the symmetric system. The regions where the primary modes and the normal secondary modes appear are determined in the space spanned by the Reynolds number and the aspect ratio.