Rayleigh-Taylor Instability
When a heavier fluid sits above a lighter one under gravity, the interface is unstable. Small perturbations grow into finger-like structures as the heavy fluid sinks and the light fluid rises, eventually producing turbulent mixing. This instability governs phenomena from supernova dynamics to oil-water separation.
γ = √(Atwood · g · k) A = (ρ₂ − ρ₁) / (ρ₂ + ρ₁) k = 2π/λ
The instability
The Rayleigh-Taylor instability occurs whenever a denser fluid is accelerated into a lighter fluid — the most familiar case being a heavy fluid on top of a light one under gravity. Lord Rayleigh analyzed the linear stability in 1883; G. I. Taylor extended the analysis to accelerating interfaces in 1950.
Growth rate
Small sinusoidal perturbations of wavenumber k grow exponentially at rate γ = √(A · g · k), where A = (ρ₂ − ρ₁) / (ρ₂ + ρ₁) is the Atwood number. Higher Atwood numbers and shorter wavelengths grow faster (until viscosity or surface tension damps the smallest scales).
Nonlinear evolution
As the fingers grow, the heavy fluid forms spikes descending into the light fluid, while the light fluid forms bubbles rising into the heavy fluid. The tips of spikes develop mushroom-shaped caps (Kelvin-Helmholtz roll-ups) due to shear along the spike edges. Eventually the flow becomes fully turbulent and the two fluids mix.
Where it appears
Rayleigh-Taylor instabilities appear in inertial confinement fusion (where they limit compression), supernovae (mixing heavy elements outward), volcanic plumes, salt domes in geology, and anywhere gravity acts on density gradients.
This simulation
This is a simplified grid-based model using advection-diffusion on a density field with buoyancy-driven velocity. It captures the qualitative features — finger formation, mushroom caps, and turbulent mixing — while running in real time in the browser.