The Kelvin-Helmholtz instability (KH instability or KHI) can occur in fluids when there is a velocity-shear, e.g., region where some of the fluid is flowing faster than fluid next to it. It can occur in a single fluid or in two adjacent fluids.
A prime example is waves on the surface of the water, e.g., ocean waves, and one sign of the instability's occurrence is a repeating, wave-like pattern. Some kinds of (Earth-weather) cloud patterns show such a repeating pattern and are in fact the results of such an instability. The visible patterns on Jupiter and Mars atmospheric surface are another.
The instability is of interest in astrophysics, including star formation, planet formation/protoplanetary disks.