Ekman Pumping Experiment

### Background:

At the end of the 19th century, Fridtjof Nansen made the observation that ice bergs in the ocean tend to drift to the right of prevailing winds. This lead one of his students, Vagn Ekman (1874 - 1954), to develop a theory explaining the role of the earth's rotation on surface currents. Over the course of his life, Ekman made a number of important contributions to the area of Geophysical Fluid Dynamics, and the process of 'Ekman Pumping' bears his name.

It is now known that boundary layers exist at the surface and bottom of the oceans. Friction with the ocean bottom (or wind stress at the surface) changes the horizontal velocity of the fluid on a depth scale of several to several tens of meters. While relatively thin, these boundary layers still play a significant role in oceanic circulation. This phenomenon also occurs in the atmosphere, and is often associated with hurricanes.

Ekman pumping (and suction) can be demonstrated in the laboratory. Water in a rapidly rotating tank will, after a time, act like a solid body. If the rate of spin is then increased, friction will act at the bottom (and sides). Because of the Coriolis force, the boundary layer fluid will exhibit radial velocities (inward or outward, depending on the sense of rotation). This net transport of fluid will then induce a circulation whereby fluid moves vertically along the side walls, as well as in the interior of the tank.

### Purpose:

To observe the dynamics of rapidly rotating systems, in particular, the process of Ekman pumping, and to measure the rate of spin-up of a homogeneous fluid.

### Experimental Set-up:

A cubical transparent tank (40 cm on each side) was filled with water to a depth of 10 cm. The tank was then rotated at a constant rate of 1.9 rad/s until the fluid reached solid body rotation. This was checked by observing the motion of small pieces of paper, floating in the water. The rotation rate was increased to approximately 2.7 rad/s and a small amount of dye was squirted at the surface of the water, in the center of the tank. Movement of the dye was observed for the next 3 - 4 minutes, after which the dye was well mixed within the fluid.

### Results:

The dyed fluid immediately acquired a downward velocity. Soon the dye reached the bottom, and one could observe a column of dyed water in the center of the tank. At points, this column separated itself into 3 or 4 clearly discernible vertical filaments, so called "Taylor columns". The dye propagated along the bottom of the tank, in the outward direction, then up the sides, and finally, some of the dye reached the center of the tank where it originated. The time of each of these events was recorded:

 TIME (sec) __________ 0 19 32 122 234 EVENT _______ dye squirted in dye reaches bottom dye reaches sides dye at the surface again dye back in the interior

A circulation had clearly been set up, whereby dyed fluid was 'pumped' down along the central axis, and then ascended up the side walls. Soon after, the dye mixed with the fluid and circulation could no longer be discerned. Moreover, the fluid seemed to have reached solid-body rotation once again. Click here to see some snapshots of this experiment.

### Analysis:

When the rotation rate increased, friction with the bottom of the tank caused fluid in the bottom boundary layer to acquire greater angular velocity. Since the rotation was cyclonic, the Coriolis force deflected this fluid outward. This net transport left a low-pressure region in the center of the tank, causing fluid from above to propagate downward. In this way a circulation was set up, which significantly decreased the spin-up time of the fluid.
 Below are several images from this experiment: A movie of this experiment is available.
Investigators:
Matt Reszka,
Richard Karsten.
Last updated by:
Bruce R. Sutherland, Sept. 98.