# Rayleigh-Taylor Instability — Heavy Fluid over Light

A heavy fluid resting on a lighter one is gravitationally unstable: any perturbation grows at rate γ = √(Agk), curling into mushroom-shaped spikes and bubbles. Tune the Atwood number, gravity, surface tension and viscosity and watch the live growth-rate curve.

> Canonical page: https://elysiatools.com/en/visualizations/rayleigh-taylor-instability

- **Category:** Physics

## Overview

Interactive Rayleigh-Taylor (RT) instability visualization. When a heavy fluid rests on a lighter one, the density gradient opposes gravity and the interface is unstable to any perturbation, which grows exponentially at the classic rate γ = √(Agk) (A the Atwood number (ρ₁−ρ₂)/(ρ₁+ρ₂), g gravity, k wavenumber). The full Chandrasekhar (1961) dispersion relation including surface tension and viscosity has the closed-form growth rate γ(k) = −νk² + √(ν²k⁴ + Agk − σk³): surface tension gives a cutoff wavenumber k_c = √(Ag/σ) stabilizing short waves, viscosity lowers the peak and shifts the most-unstable mode to longer wavelengths, and the nonlinear regime crosses over to constant-velocity Layzer mushroom spikes and bubbles. A reduced-order multi-mode interface model (Fourier cosine modes evolved with RK4 under Landau cubic saturation daₙ/dt = γₙaₙ − λkₙ²aₙ³) plus the potential-flow perturbation streamfunction advects dye tracers to render the characteristic mushroom roll-up. Three visualization panels: (1) Main animated scene showing the heavy fluid (red) above the light fluid (blue) with the live evolving interface, the two region fills, dye-tracer particles advected by the unstable-mode velocity field revealing mushroom-shaped spikes (falling) and bubbles (rising), and a gravity arrow. (2) Growth Rate γ(k) plot showing the solid blue growth curve with the most-unstable mode k* peak marked, the dashed orange inviscid √(Agk) reference, and the surface-tension cutoff k_c dashed line. (3) Amplitude vs Time log-scale plot showing the measured dominant-mode growth (solid blue, straight-line slope = measured γ) against the theoretical ln(a₀)+γt line (dashed orange), with the late-time Landau saturation bend. Adjustable parameters: Atwood number A (0.05–0.95), gravity g (0–2), initial perturbation a₀ (0.001–0.5), surface tension σ (0–0.5), kinematic viscosity ν (0–0.2). Six scenario presets: Classic Mushroom, Supernova (A=0.9 violent growth), Nuclear Fireball (A=0.8 strong drive), Water/Oil (lab A=0.3 with surface tension), Viscous Honey (high viscosity, damped), Tension Damped (strong surface-tension cutoff). Real-time statistics: regime (RT unstable / Astrophysical / Viscous RT / Tension cutoff / Stable), peak growth rate γ*, most-unstable k*, e-folding time 1/γ*, measured γ from log-fit, and cutoff k_c. Educational content covers the RT mechanism (Rayleigh 1883, Taylor 1950, heavy-over-light stores gravitational potential energy like an upside-down pendulum), the Chandrasekhar cutoff and nonlinear Layzer saturation, and applications (nuclear-fireball mushroom filaments, core-collapse-supernova blast-wave RT fingers enriching the galaxy and directly observed in the Crab Nebula, ocean salt fingering, inertial-confinement-fusion ablation front, oil-and-water mixing). Multi-language support (zh, en, es, fr, de, ru, pt).

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