The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) can occur when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the interface between two fluids. An example is wind blowing over water: The instability manifests in waves on the water surface. More generally, clouds, the ocean, Saturn's bands, Jupiter's Red Spot, and the sun's corona show this instability.
When two superposed fluid layers of different physical parameters move parallel to each other with a relative horizontal velocity, the instability of the plane interface between the two fluids is called Kelvin-Helmholtz instability. The Kelvin-Helmholtz instability occurs in various situations such as wind blowing over the ocean, meteor entering the earth atmosphere and in oil exploration industry etc.
For derivation purpose, please use
Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability, Dover publications, New York, 1981.
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