Motion of a Light Free Sphere and Liquid in a Rotating Vertical Cylinder of Finite Length

Abstract

The paper is devoted to an experimental study of the fluid motion excited by a light spherical body floating along the axis of a rotating vertical cylinder. The experiments are performed with fast rotation. The high-speed video recording examines the behavior of the body depending on the rotation rate and liquid viscosity. PIV-method is used to investigate the velocity fields of liquid. In the cavity frame, the body excites the motion liquid in the form of a Taylor–Proudman column, the diameter of which is consistent with the body diameter. In the upper column, the liquid performs a retrograde differential rotation, and in the lower, a prograde one. Outside the columns, the differential rotation is practically absent. It is found that the intensity of the retrograde azimuthal motion in the frontal column increases as the body goes up, while the intensity of the prograde rotation in the rear column decreases. As a result, the free body simultaneously with motion along the axis performs differential rotation: in the lower part of the cavity it is prograde, while in the upper one it is retrograde. The intensity of the body differential rotation varies with the longitudinal coordinate linearly and decreases with the dimensionless rotation velocity.

Keywords

• rotation
• spherical body
• Taylor–Proudman column
• motion velocity
• differential rotation