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Contributed by H. Hornung
Origin unknown

A special form of instability is seen in this cloud formation. When two streams are in parallel motion, but there is a velocity difference between them, a shear layer forms. The shear layer is generally unstable, in that a small perturbation, once formed, will continue to grow. The mechanism can be explained by considering the shear layer as a thin sheet, where the velocity changes suddenly. If the sheet develops a small bump, say on the high-speed side, then the streamlines on the high-speed side in the neighbourhood of the bump get closer together, and by Bernouli's equation the pressure must decrease locally. At the same time, the streamlines on the low-speed side get further apart, and the pressure increases. So there is a resultant force acting on the sheet which tends to increase the size of the bump. We see that a bump, once formed, naturally tends to grow. That is, the shear layer is unstable. As the perturbation on the sheet grows, it tends to roll-up, as in the picture of these clouds, where water vapor has made the shear layer visible. This particular type of instability is known as the Kelvin-Helmholtz instability, and it can be seen in the initial stages of the roll-up of a shear layer. It continues to be a feature of the structure of free shear layers, even at very high Reynolds numbers, and it is commonly seen in many flows.

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