Kelvin–Helmholtz waves are internal gravity waves that occur in a stably stratified fluid when the density decreases with height. The name comes from Lord Kelvin and Hermann von Helmholtz, who were both working on the problem of wave propagation in fluids at the same time. These waves can be thought of as two-dimensional versions of sound waves, and they play an important role in the dynamics of Earth’s atmosphere and oceans.
Kelvin–Helmholtz instability is a type of instability that can occur when there is a velocity shear between two layers of fluid. This can happen, for example, when wind blows over water or when cold air flows over warm air. If the velocity difference is large enough, it can cause the layers to mix, which leads to the formation of Kelvin–Helmholtz waves.
The most famous example of Kelvin–Helmholtz waves is probably the “cat’s eye” cloud pattern that sometimes forms in cirrus clouds. These clouds are made up of ice crystals, which are much denser than air. When strong winds blow across them, they can create a rippling effect known as “Kelvin wake.”
There are many other examples of Kelvin–Helmholtz instabilities in nature. For instance, they often occur at the boundary between two different fluids, such as oil and water. They can also happen inside liquids, such as blood vessels or lava flows. In each case, the instability results in mixing between the two fluids and the creation of distinctive patterns.