Rayleigh-Taylor Instability

Heavy fluid over light — linear growth σ ~ √(Akg), nonlinear spikes & bubbles

Linear Growth Rate σ vs Wavenumber k

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Growth rate: σ(k) = √(Akg − σ_s k³/((ρ₁+ρ₂)))
Atwood number: A = (ρ₂−ρ₁)/(ρ₂+ρ₁). Surface tension stabilizes short wavelengths. Critical wavenumber: k_c = √(A g(ρ₁+ρ₂)/σ_s)

Interface Evolution — Nonlinear Regime

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Nonlinear regime: bubbles (light fluid rising) have terminal velocity v_b ~ √(AgR) where R is bubble radius. Spikes (heavy fluid falling) accelerate indefinitely (A→1). Bubble merger leads to self-similar cascade.

2D RT Simulation — Spectral Method

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Pseudo-spectral simulation of incompressible RT instability using sharp-interface model. Grid evolves the interface η(x,t) from a multi-mode perturbation η₀(x) = Σ aₙ cos(nkx). Color: heavy fluid (blue) sinks, light fluid (amber) rises.

Atwood Number Dependence

Mixing Layer Width ~ √(Agt²)

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