Magnetically Induced Rotating Rayleigh-Taylor Instability

We present a protocol for preparing a two-layer density-stratified liquid that can be spun-up into solid body rotation and subsequently induced into Rayleigh-Taylor instability by applying a gradient magnetic field.

The overall goal of this experiment is to observe the effect of rotation on a gravitationally unstable system comprised of a dense fluid overlying a less-dense fluid. This method can help answer key questions in fluid dynamics, such as how the stabilizing effect of rotation competes and interacts with the destabilizing effect of gravity. This technique's main feature is the ability to create a stable rotating, two-layer system and then use a magnet to manipulate the effective weights of each layer, triggering the instability.

This is the apparatus used for the experiment. The principle visible components are a rotating platform for the experimental tank, a copper cylinder that supports it, and a room-temperature bore superconducting magnet. The cylinder descends into the bore of the magnet and a 1.8 tesla magnetic field.

This schematic provides additional details of the arrangement. The rotation of the platform is produced by an off-axis motor that turns a slip bearing with a keyhole orifice. The copper cylinder is attached to the key-shaped drive shaft and descends under its own weight when the holding pin is removed.

The complete set-up includes the lighting and a remote-controlled camera to capture images. With the tank in position on the platform, move the drive shaft to its lowest position. Ensure the video camera will have a view of the experiment that is in-focus and appropriately lit.

To prepare for the experiment, place the platform and copper cylinder in their highest position. Lock the cylinder in place with the holding pin. With everything else set, remove the tank to prepare it for the experiment.

At a lab bench, begin to prepare the liquids for the tank. For the dense layer, begin with 250 milliliters of room-temperature distilled water, and add approximately 6.25 grams of sodium chloride to the water. The components of the light upper layer are 325 milliliters of room-temperature distilled water, along with manganese chloride and red and blue water tracing dyes.

Add a small quantity of fluorescein sodium to complete the preparation. The two fluids are now ready for the experiment. The stratified liquids will be held in a clear cylindrical container, which has a lucite lid that can fit into it.

The lid has bleed holes to allow fluid and air to flow through. In addition to the container and fluids, have a flotation boat ready for use. The flotation boat consists of styrene walls on a sponge base.

The bottom of its interior should be lined with strong tissue paper. The boat should be able to easily fit into the experimental tank without touching the sides. Proceed with the next steps only when ready to perform the experiment.

Start with the high-density fluid and begin to add it to the tank. Stop when 300 milliliters has been added. Next, prepare a header tank with a clamp and tubing for the low-density fluid.

The header tank should hold at least 350 milliliters and the clamp should allow for control of the fluid flow. Proceed by adding low-density fluid to the header tank. Then, mount the header tank above the experiment tank to allow the release of fluid near the high-density fluid surface.

Place the flotation boat onto the high-density fluid surface. Adjust the clamp on the header tank to add low-density fluid to the flotation boat, and add about three milliliters per minute. With time, the low-density fluid diffuses through the sponge forming a light fluid layer above the high-density fluid.

As the boat lifts away from the interface, gradually increase the flow rate. Keep filling until the header tank has been emptied. Once the fluid has been completely siphoned, remove the flotation boat slowly to minimize dripping and get the lid for the experiment tank.

Put the lid in place, and start to lower it into the upper layer of fluid. Stop when the depths of each layer are equal, and there are no trapped air bubbles. If successful, there will be two layers of fluid of equal depth with a sharp interface between them.

There will also be a layer of low-density fluid on top of the lucite lid. Proceed quickly to perform the experiment and carefully move the tank to the apparatus. Place the experimental tank on the platform, while keeping it far away from the magnet.

Turn on the motor and increase the rotation rate slowly by increasing the power-supply voltage until the desired rate is reached. Once the desired rotation rate is reached, start video-recording and get into position to remove the holding pin. When ready, remove the pin and allow the tank to descend into the magnetic field.

These images are snapshots of the fluid interface for four different rotation rates. Each column corresponds to a different time and increases in increments of half a second. At early times, for example at the one-second mark, for each rotation rate, there is a perturbation to the interface with a dominant length scale.

With increasing rotation rate, the width of the snake-like structures decreases. These images are from a series of experiments with varying fluid viscosity and a fixed rotation rate. Each column corresponds to a different time.

The observed length scale of the instability increases as the viscosity increases from lower values to higher values. By plotting the dominant radio wave length as a function of the rotation rate, a lower threshold for the scale of the instability becomes observable. In this data for fluid layers with the approximate viscosity of water, above rotation rates of about four radians per second, the lower threshold is approximately six millimeters.

Once mastered, this technique can be carried out in one hour if it is performed properly.