Heavy fluid over light — growth rate σ = √(Akg) at wavenumber k
Growth rate: —
Rayleigh-Taylor instability occurs when a dense fluid sits above a lighter one in a gravitational field.
Perturbations grow exponentially: σ(k) = √(Akg − Tk³/(ρ₁+ρ₂)) where A = (ρ₂−ρ₁)/(ρ₂+ρ₁) is the Atwood number.
Surface tension stabilizes short-wavelength modes; the fastest-growing mode kmax = √(Aρg/3T) sets the dominant scale.
The nonlinear stage produces characteristic mushroom-cap "bubbles" rising into the heavy fluid.