In general, the condition for linear instability is that the imaginary part of the "wave speed" c is positive. Finally, restoring the surface tension makes c2 less negative and is therefore stabilizing. Indeed, there is a range of short waves for which the surface tension stabilizes the system and prevents the instability forming. When the two layers of the fluid are allowed to have a relative velocity, the instability is generalized to the Kelvin–Helmholtz–Rayleigh–Taylor instability, which includes both the Kelvin–Helmholtz instability and the Rayleigh–Taylor instability as special cases. It was recently discovered that the fluid equations governing the linear dynamics of the system admit a parity-time symmetry, and the Kelvin–Helmholtz–Rayleigh–Taylor instability occurs when and only when the parity-time symmetry breaks spontaneously. Vorticity explanation The RT instability can be seen as the result of baroclinic torque created by the misalignment of the pressure and density gradients at the perturbed interface, as described by the two-dimensional inviscid vorticity equation, , where ω is vorticity, ρ density and p is the pressure. In this case the dominant pressure gradient is hydrostatic, resulting from the acceleration. When in the unstable configuration, for a particular harmonic component of the initial perturbation, the torque on the interface creates vorticity that will tend to increase the misalignment of the gradient vectors. This in turn creates additional vorticity, leading to further misalignment. This concept is depicted in the figure, where it is observed that the two counter-rotating vortices have velocity fields that sum at the peak and trough of the perturbed interface. In the stable configuration, the vorticity, and thus the induced velocity field, will be in a direction that decreases the misalignment and therefore stabilizes the system. Late-time behaviour The analysis in the previous section breaks down when the amplitude of the perturbation is large. The growth then becomes non-linear as the spikes and bubbles of the instability tangle and roll up into vortices. Then, as in the figure, numerical simulation of the full problem is required to describe the system. See also Saffman–Taylor instability Richtmyer–Meshkov instability Kelvin–Helmholtz instability Mushroom cloud Plateau–Rayleigh instability Salt fingering Hydrodynamic stability Kármán vortex street Fluid thread breakup Notes References Original research papers (Original paper is available at: https://www.irphe.fr/~clanet/otherpaperfile/articles/Rayleigh/rayleigh1883.pdf .) Other xvii+238 pages. 626 pages. External links Java demonstration of the RT instability in fluids Actual images and videos of RT fingers Experiments on Rayleigh–Taylor instability at the University of Arizona plasma