RayleighTaylor

The Rayleigh–Taylor instability, or RT instability, is a hydrodynamic instability of the interface between two immiscible or miscible fluids of different densities when the lighter fluid is accelerated into the heavier. This occurs under gravity or any acceleration opposite to the density gradient, such as a dense fluid atop a lighter fluid in a gravitational field.

In the idealized case of incompressible, inviscid fluids with a sharp interface and negligible surface tension, small perturbations at the interface grow exponentially with a growth rate gamma given by gamma = sqrt(A g k), where A is the Atwood number (rho2 − rho1)/(rho2 + rho1), g is acceleration, and k is the perturbation wavenumber. Surface tension and viscosity modify the growth, stabilizing short wavelengths and damping the instability: gamma^2 = A g k − (sigma/(rho1 + rho2)) k^3, with further viscous terms. Thus small wavelengths can be stabilized if surface tension is large or the fluids are highly viscous.

Nonlinear development leads to characteristic structures known as bubbles rising into the heavy fluid and spikes of the heavy fluid penetrating downward, producing complex mixing and finger-like patterns. The late-time state can become turbulent and self-similar, depending on the fluids and conditions.

Historically, the instability was studied by Lord Rayleigh in 1883 and independently by G. I. Taylor in the 1950s. It has broad relevance in astrophysics, inertial confinement fusion, supernova remnants, and other high-energy-density and geophysical flows.