Category Archives: Kelvin-Helmholtz waves

Breaking waves aren’t just for the ocean

When thinking of the ocean, we visualize the beautiful waves. Wind in the lower atmosphere moves over the water below, creating waves that build and break along the shore.

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Photo courtesy of the Bureau of Ocean Energy Management

This is a familiar example of fluids (both the ocean and the atmosphere) with two different densities moving relative to one another, with the waves being created along the interface between these two fluid layers. This isn’t the only place, though, where these breaking waves can be seen. Take for example this recent picture from Jan Todo Russell over Seattle, Washington. Notice the similarity to the breaking ocean wave?

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Jan Todo Russell, Seattle, Washington, 26 Mar 2015

This wave pattern in the clouds, similar to that on the ocean surface, is due to Kelvin-Helmholtz instability, named after Lord Kelvin and Hermann von Helmholtz. In order to understand this instability, consider two layers with different densities on top of each other. The lighter (less dense) layer sits atop the heavier layer (think of the way less dense oil sits atop water). Not only do these layers have different densities, but they are also moving at different speeds. This leads to what is called “velocity shear” across the interface between the two fluids.

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Because of the higher velocities in the layer above, a small disturbance can form along the interface of the two fluids. The higher velocity air can, in a sense, grab the lower velocity/denser air below, allowing these disturbances to grow and eventually breaking over like an ocean wave crashing ashore. This ultimate causes turbulent mixing of the two layers, which is a more stable scenario than the separated layers previously observed.

This instability has been studied many times in computer-based and laboratory experiments. Equations have been derived to describe this instability and to determine the necessary conditions (the thresholds) for this instability to occur. Applying these equations in numerical simulations on computers allows for these waves to be produced and studied, such as in this example from the Hrenya Research Group at the University of Colorado, who describe this instability as “An aesthetically pleasing unstable behavior seen in traditional fluids.”

KHI_videoIn addition, lab experiments have been set up where this shear zone is established between two layers of different densities. By tilting these fluids, the upper-most, light fluid flows faster, eventually leading to this KH instability and creating the waves, such as in this video from the Department of Applied Mathematics and Theoretical Physics (DAMTP) of the University of Cambridge.

So what does this have to do with the atmosphere? Well, you can have vertical layers in the atmosphere with different densities, where the upper layer has faster wind speeds. This can lead to disturbances atop cloud layers, that lead to this instability and create Kelvin-Helmholtz wave clouds in the sky. Here are a few more dramatic examples from our Community Cloud Atlas.

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Brenda Dolan, Colorado

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Scott Ellis, Colorado

This instability isn’t unique to our atmosphere and oceans. This instability is out of this world with this wave pattern viewed along the edges of the magnetospheres of planets, including our own Earth and Mercury (see below), as well as in the vicinity of the Red Spot of Jupiter! Nature is amazing!

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Great Red Spot on Jupiter (courtesy of NASA)

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A figure from the published 2013 article in Nature Communications titled Dawn–dusk asymmetry in the Kelvin–Helmholtz instability at Mercury (Jan Paral and Robert Rankin): doi:10.1038/ncomms2676. The colors show the ion density of Mercury’s magnetosphere, where you can see the KH waves along the edge due to the solar wind.

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