In this experiment anti-cylconic and cyclonic flow is induced in the Spin Tank by
speeding up the rotational rate to produce anti-cyclonic flow and slowing down the
rotational rate to produce cyclonic flow. The rough bottom of the tank produces a
stress with the water immediatley above it (the height of the water affected by the
stress can be calculated by predicting the Ekman Depth) and an Ekman flow is
induced 90 degrees to the right of the stress
Anti-Cyclonic Flow
As the rotating table moves counter-clockwise, the water which
is in solid body rotation moves counter-clockwise as well. When
the rotational rate is increased a stress is induced in the same
direction as the flow. The faster moving rough bottomed surface of
the tank produces friction with the overlying water up to the height
of the Ekman layer. Since the direction of the stress is parallel
to the motion of the fluid, an Ekman flow is induced 90 degrees to
the right of the stress. The direction of the Ekman flow should be
towards the outside of the tank.
To run this experiment
1) Fill the tank to 10cm of water
2) Set the period of rotation to 10.5 seconds per revolution
3) Allow fluid to achieve solid body rotation (Approx. 20 minutes)
4) Drop in a few crystals of Potassium Permanganate
5) Note the Taylor Columns
6) Increase the rotational rate to 7 seconds per revolution.
Note:
The markers appear to move clock-wise as the rotational rate of the table is increased. Initially the
water and floating markers are in solid body rotation with the tank. However when the rate of rotation
of the tank and its mounted camera is increased, the water that is not in the Ekman layer, and therefore
not feeling the immediate effects of friction with the tank's bottom, now rotates slower than the tank and
camera. This leads to the illusion that the markers are rotating clock-wise when they are in fact just
rotating counter-clockwise at a slower rate than the tank and camera.
Cyclonic Flow
A cyclonic flow is formed when the rotational rate of the table is slowed down.
This creates a stress in the direction opposite to the flow of the overlying water,which
moves faster than the rough bottomed surface below it. The Ekman flow is 90 degrees to
the right of the induced stress. Theoretically direction of the Ekman flow should be directly
inwards toward the center of the tank.
To run this experiment
1) Fill the tank to 10cm of water
2) Set the period of rotation to 7 seconds per revolution
3) Allow fluid to attain solid body rotation (approx. 20 minutes)
4) Drop is crystals of Potassium Permanganate into the tank
5) Note the Taylor Columns
6) Slow the rotational rate by turning off the motor
Note:
The floating markers appear to suddenly start rotating counter-clockwise when the motor is turned off.
This apparent motion is due to the fact that the water and floating markers are in solid body rotation
with the tank and its mounted camera. When the motor is turned off, and rotation of the tank and camera
is stopped, the water that is above the Ekman layer continues to rotate counter-clockwise. Although it
appears that the floatings markers suddenly start to rotate counter-clockwise when the motor is turned
off, it is actually that the camera has stopped rotating.
Calculating the height of the Ekman Layer
The height of the Ekman layer below corresponds to a period of 10.5 s
δ : Depth of the Ekman Layer (m)
ν : Molecular Viscosity
Ω : Rotation rate (1/seconds)
