Kelvin–Helmholtz instability

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. Hermann von 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.

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Stability

  For some short enough wavelengths, if surface tension can be ignored, two fluids in parallel motion with different velocities and densities will yield an interface that is unstable for all speeds. 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. Also the study of this instability becomes applicable to inertial confinement fusion and the plasma–beryllium interface.

The classic textbooks by Subrahmanyan Chandrasekhar and Drazin & Reid consider the KH and RT instabilities in much detail.

See also

• Fluid mechanics
  • Fluid dynamics

References

• Kelvin, Lord (William Thomson), "Hydrokinetic solutions and observations," Philosophical Magazine, vol. 42, pages 362–377 (1871).
• Helmholtz, Hermann Ludwig Ferdinand von, "Über discontinuierliche Flüssigkeits-Bewegungen [On the discontinuous movements of fluids]," Monatsberichte der Königlichen Preussiche Akademie der Wissenschaften zu Berlin [Monthly Reports of the Royal Prussian Academy of Philosophy in Berlin], vol. 23, pages 215 ff (1868).