• M. A. Alkhadra

Kelvin–Helmholtz Instability

As we saw with the Rayleigh–Taylor instability, the Kelvin–Helmholtz instability manifests beautifully in several astronomical phenomena, which include the bands of Saturn, the Great Red Spot of Jupiter, and the corona of our sun. This hydrodynamic instability arises due to either a shearing (tangential) force in a single continuous fluid or a difference in velocity across the interface separating two distinct (typically immiscible) fluids. A familiar example of the Kelvin–Helmholtz instability is wind blowing over water; this instability may also be seen in clouds that resemble breaking ocean waves. The characteristic wave structure of clouds appears when two different layers of air in the atmosphere travel at unequal speeds. The light upper layers of air generally travel faster than the dense lower layers and, in a sense, “scoop” the top surface of the cloud in a wave-like rolling motion.

The Kelvin–Helmholtz instability was studied by European physicists Lord Kelvin and Hermann von Helmholtz in the 19th century. Helmholtz, in particular, examined the observable effect of a small disturbance, such as a wave or vibration, introduced at the interface separating two fluids of unequal density. A difference in density, however, is not a necessary condition for the onset of instability and transition to turbulence. The development of the Kelvin–Helmholtz instability in fact only requires the existence of a uniform shearing force at the interface between the two fluids. The Kelvin–Helmholtz instability also differs from the Rayleigh–Taylor instability—where no shearing forces are present—in that the latter is caused by gravity. It is now time to marvel at the beauty of the simple, yet elegant Kelvin–Helmholtz instability as it appears in our natural universe.

Figure 1. A false-color image of the Great Red Spot in the atmosphere of Jupiter taken from Voyager 1, the space probe launched by NASA in the 1970s. The wave-like pattern below the Great Red Spot is characteristic of the Kelvin–Helmholtz instability. (For scale, the white ovoid storm directly underneath the Great Red Spot has the approximate diameter of Earth.)

Figure 2. A Cassini (spacecraft) image taken by NASA that shows the turbulent boundary between two latitudinal bands in the atmosphere of Saturn. This boundary curls repeatedly along its edge forming the pattern characteristic of the Kelvin–Helmholtz instability, which is indeed a fairly common phenomenon on gas-giant planets given their wide temperature distributions and alternating jets.

Figure 3. Photograph image of the Kelvin–Helmholtz instability as it manifests in clouds.

Figure 4. Another photograph image of the Kelvin–Helmholtz instability as it manifests in clouds.

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