Flow of an incompressible fluid in a partially filled, rapidly rotating cylinder with a differentially rotating endcap

The flow in a partially filled, strongly rotating cylinder with a differentially rotating endcap was studied both experimentally and numerically. The cylindrical container was mounted with a vertical axis of rotation, partially filled with an incompressible fluid, and rotated at a sufficiently high angular velocity that the fluid formed a film of essentially uniform thickness on the sidewall of the container. An axial circulation in this fluid film was induced by the differential rotation of one of the container endcaps. A laser-Doppler velocimeter was used to measure the axial and azimuthal velocity components. The experimental results were compared with a finite-difference model of the flow, and the agreement between the two was good. Boundary layers of thickness proportional to cu rt E, where E = nu/Omega L2 is the Ekman number, are found both at the lateral wall and at the vertical free surface. The existence of cu-rt-E boundary layer along the free surface is due to the invariant structure of the sq-rt-E Ekman layers on the horizontal surfaces with respect to a free surface. The radial transport in the Ekman layers of a partially filled rotating cylinder is essentially the same as that in a completely filled container. The axial transport, which in a completely filled container would have occurred in the volume now occupied by an empty core, is instead confined to a thin boundary layer along the free surface.