Here’s another trajectory, showing some of the transient behavior that occurs when the drum is first switched on

The above movie is a 52 minute recording compressed to play in 2:40 and illustrate the complexity of motion shown by this seemingly simple system.

 

The experiment involves a plexiglass drum, oriented horizontally, and spinning on the horizontal axis.  The drum is filled with pure glycerine and three stainless steel ball bearings, one-half inch in diameter.  As the drum is rotated, the ball bearings are dragged up the side of the container.  If the drum is spun fast enough, the ball bearings will move up the wall until gravity pulls them away, at which point they will fall through the fluid until contacting the wall again.  At low rotation rates, this cascading is periodic and predictable.  At very high rotation rates, centrifugal force holds the particles in a fixed position relative to the plexiglass cylinder.  However, at some intermediate speed, the particles begin to wander erratically in the horizontal (x) direction while also cascading in the y-z plane.

 

Reynolds numbers in this experiment are moderate, usually between 1 and 10.  Thus, turbulence is not important, but long-range fluid effects almost certainly are.  The drum is spinning fast enough that the fluid within is not undergoing rigid body rotation.