A rotating fluid is 'stiffened' in the direction of the rotation axis. Here
we are looking down on such a fluid in a plexiglass cylinder on a rotating
platform (the outer circle is the cylinder). A smaller flat plexiglas disk
(smaller faint circle) sits on top of the water and spins slowly
counterclockwise (cyclonically) relative to the counterclockwise
rotation of the cylinder.
This causes the fluid beneath the disk to spin at about 1/2 the rate of
the disk, as if feels Ekman layer drag on the bottom as well as at the top
disk. At very slow speeds a symmetrical viscous-driven overturning
circulation transmits the disk rotation through the fluid column (see notes
on overturning circulations elsewhere on this site). There is a
cyclindrical viscous boundary layer just beneath the rim of the disk in
which the fluid circulates downward. The overturning cell involves radially
outward motion in the thin (~1mm thick) viscous boundary layer beneath the
disk, downward in a somewhat thicker viscous shear layer beneath the rim,
inward at the bottom and upward in a very gentle flow beneath the disk.
However, at higher speeds (image above) the circular motion is
unstable and sets of eddies form at
the edge of the disk, the number depending on the disk speed.
For rotation
in the opposite direction (anticyclonic disk rotation, above)
a 'tripole'
forms in
which the inner core is joined by two large eddies at its edges.
This kind of steady nonlinear flow is interesting, because it does not
break down into turbulence, but is a well-organized way the fluid finds to
transmit the stress of the upper disk through the fluid to the rigid bottom
of the cylinder. See Hide and Titman, Journal of Fluid Mechanics, 1967, and
John Hart's website
at University of Colorado,
-Peter Rhines viii2003
