Rayleigh–Taylor instability

The Rayleigh-Taylor Instability (RTI ) is a hydrodynamic instability, which can grow exponentially a disturbance at the interface of two different heavy liquids. It is named Lord Rayleigh and Geoffrey Ingram Taylor after the two physicists.

Description and occurrence

RTI is a two-phase instability (as the Kelvin-Helmholtz instability ), which occurs when two different density liquids are mutually accelerated. It does not matter which way is the acceleration. Thus, a heavy liquid to a light in a gravitational field Rayleigh-Taylor unstable, but also the envelope of an exploding as a supernova star, which is accelerated towards the thinner interstellar medium. The frayed appearance of the Crab Nebula, for example, a result of RTI. Typical of the mushroom-shaped protrusions are the RTI of the fluids into each other may be observed, for example, with the addition of some milk in a cup of tea.

Theory

From the linear stability analysis of the fluid dynamics equations the following dispersion relation is obtained for two adjacent, of different density, did not move liquids:

Here, the angular frequency of the disturbance, its wave number, the acceleration ( for example, gravitational ) and the ratio of the densities of the liquid layers.

If, that is, the overhead liquid is heavier, so is imaginary, ie inserted into the wave equation of the disturbance obtained an exponential increase in the disorder. The configuration is therefore unstable to the smallest disturbances. In the opposite case ( light liquid to severe ) is obtained by the way the dispersion relation for surface waves.