RTX

Ekman Flow Visualization and Experimental Observation

Mock-up Diagram of Flow:

The Ekman spiral flow at a top boundary in the in the northern hemisphere is known to turn clockwise (anticlockwise in the southern hemisphere) as depth increases. At an air-water interface with a constant, uniform wind blowing across the top of the water, the no-slip boundary condition demands that the water be dragged along with the air at the very surface. The Coriolis effect then turns the fluid flow to the right of the velocity (left in the southern hemisphere, which is how we get the anticlockwise spiral). As you look deeper, the viscous drag force and Coriolis effect turn the fluid flow even further to its right (or left) until you get to the scale height of the Ekman layer. A quick diagram depicts a wind-driven Ekman spiral in an air-water system in the northern hemisphere.


Image credit: http://en.wikipedia.org/wiki/Ekman_layer.

The Black hollow arrows on the top left are the wind flow along the water surface and the red arrows are the resulting Ekman flows forming the spiral as depth z increases. At the bottom is a projection of the spiraling Ekman flow velocity into the horizontal plane. The spiral at the bottom of a fluid flow, e.g. at the bottom of a rotating tank, turns the other way due to the direction of the viscous drag forcing at the no-slip boundary being in the opposite direction of the flow. The same thing happens in the air above the air-water interface: the Ekman spiral turns counterclockwise as distance from the interface increases (in the southern hemisphere, this turns clockwise).


Flow Visualization Experiments:

Using the apparatus built, I conducted several preliminary experiments aimed at demonstrating the discussed Ekman flow phenomena. Please note that these experiments may not best illustrate only Ekman flows as there are many other fluid flow phenomena occurring in the tank at the same time; I invite you to come and play experiment for yourself!

In the following videos, the view is co-rotating with the tank at an approximate 5 rpm. The water is in solid-body rotation when the dye is added. The rotation rate is then slowed to about 3 rpm to set up a rotating flow over the bottom of the tank. In the boundary region at the bottom, an Ekman layer forms creating streaks in any dye that is present. These streaks follow the Ekman spiral structure.

This attempt did not illustrate the Ekman spiral flow structure very well since not much of the inserted dye did not fall to the bottom of the tank before the rotation speed was changed. This resulted in many things happening that were not the Ekman flow, obstructing our view of the two of three "streaks" that did form.

The same approach was taken for this video. This time the tank was filled with warm water and the dye mixed with cool water and inserted via pipette to encourage dye sinkage. Improvements still need to be made, namely the dye needs to be released at the bottom of the tank. The nature of the no-slip boundary condition tends to discourage flows that reach the bottom of the tank.

I used a GoPro Hero2 camera (with a WiFi control module installed) mounted above the tank to record my experiments. Final Cut Pro was used to white balance the video and add annotations. Thanks to YouTube for easy video hosting!