# Rayleigh-Taylor Instability

on . Posted in Fluid Dynamics

Rayleigh-Taylor instability, abbreviated as $$\gamma$$  (Greek symbol gamma), is a fluid instability that occurs at the interface between two fluids of different densities when the lighter fluid is pushing against the heavier fluid.  This instability leads to the interpenetration and mixing of the two fluids.  The instability is driven by the gravitational force acting on the density difference between the two fluids.  When the heavier fluid is positioned above the lighter fluid, the gravitational force tends to cause the interface between them to become unstable. Small perturbations at the interface grow over time, leading to the formation of irregularities, spikes, and bubbles in the interface.  These structures eventually result in the mixing of the two fluids.

Rayleigh-Taylor instability can be observed in various natural and laboratory settings, including astrophysics, geophysics, and fluid dynamics experiments.  In astrophysics, for example, it plays a role in the dynamics of supernovae explosions and the behavior of stars.  In the laboratory, researchers often study Rayleigh-Taylor instability to understand fluid dynamics, turbulence, and mixing processes.

### Rayleighâ€“Taylor instability Formula

$$\gamma = \sqrt{ A \; g \; \alpha }$$

$$A = \gamma^2 \;/\; g \; \alpha$$

$$g = \gamma^2 \;/\; A \; \alpha$$

$$\alpha = \gamma^2 \;/\; A \; g$$

Symbol English Metric
$$\gamma$$  (Greek symbol gamma) = Rayleighâ€“Taylor instability $$1\;/\;sec$$  $$1\;/\;s$$
$$A$$ = Atwood number $$dimensionless$$ $$dimensionless$$
$$\alpha$$  (Greek symbol alpha) = special wavenumber $$1\;/\;ft$$ $$1\;/\;m$$
$$g$$ = standard gravity $$ft\;/\;sec^2$$ $$m\;/\;s^2$$

Tags: Fluid