Rayleigh-Taylor instability

Principle of Rayleigh-Taylor instability
Manifestations of Rayleigh-Taylor instability


Principle of Rayleigh-Taylor instability

    This instability, also called Richtmyer-Meshkov instability, shows the competition between surface tension and gravity.
 
 

Scheme of the domain for Rayleigh-Taylor instability
Rayleigh-Taylor experiment

 

    Consider two fluids of different densities, the heaviest above the lightest. An horizontal interface separates the two fluids. This situation is unstable because of gravity. Effectively, if the interface is modified then a pressure want of balance grows. Equilibrum can be found again tanks to surface tension that's why there is a competition between surface tension and gravity.
    Surface tension is stabilizing instead gravity is unstabilizing for this configuration.
 
 

Visualisations of Rayleigh-Taylor instability
 

Click here for animation (1) (.mpg)
Click here for animation (2) (.mpg)

    In some case we can see for such instability "fingers" of upper fluid inside lower fluid.
 
 

2D fingers in Rayleigh-Taylor instability
3D fingers in Rayleigh-Taylor instability

 
 
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Manifestations of Rayleigh-Taylor instability

    This kind of instability can be found in a lot of problems linked to interface in physicochemical domains : polyphasic hydrodynamics where there are liquid, solid and vapour phases with or without miscibility or phase changes ; watering ; displaying film ... Rayleigh-Taylor instability is then very usefull.
    We can also speak about interactions between pressure waves and flamm surfaces, super and hypersonic combustion, interaction laser-matter ... Like Kelvin-Helmholtz instability, this one presents also a "violent" characteristic which can lead to destruction of devices.

    An example of Rayleigh-Taylor instability we can see in our daily life is the example of a column of liquid which develops corrugations in its shape and ultimately breaks into discrete drops : it is the example of water jet coming from a tap.

Evolution of the fluid 

    The basic state is a cylindrical column of liquid (1). The column retains its circular cross-section but with diameter varying along its lenght (2). The changed surface curvature will produce a change of pressure within the jet needed to balance the action of surface tension. Then, the external pressure is a maximum where the section is minimum (a) and a minimum where the section is maximum (b). The pressure gradient thus pushes fluid in direction that amplify the original disturbance.
    Lastly, the water jet breaks-up into discrete drops (3).

Jet breaking into drops

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