Kelvin-Helmholtz instability
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Kelvin-Helmholtz instability can occur when velocity shear is present within a continuous fluid or when there is sufficient velocity difference across the interface between two fluids. The theory can be used to predict the onset of instability and transition to turbulent flow in fluids of different densities moving at various speeds. Helmholtz studied the dynamics of two fluids of different densities when a small disturbance such as a wave is introduced at the boundary connecting the fluids.
For two fluids in parallel motion with different velocities and densities, the interface will be unstable for all speeds, for some short enough wavelengths, if surface tension can be ignored. The existence of surface tension stabilises the short wavelength instability however, and theory then predicts stability until a velocity threshold is reached. The theory with surface tension included broadly predicts the onset of wave-formation in the important case of wind-over-water.
For a continuously-varying distribution of density and velocity, (with the lighter layers uppermost, so the fluid is RT-stable), the onset of the KH-instability is given by a suitably-defined Richardson number. Ri Typically the layer is unstable for Ri<0.25. These effects are quite common in cloud layers.
The classic textbooks by Chandrasekhar and Drazin & Reid consider the KH & RT instabilities in much detail.