Rayleigh-Taylor Instability

What you are seeing: a dense fluid (red) sitting above a lighter fluid (cyan) in a downward gravitational field. Any perturbation grows as $\exp(\sigma t)$ with $\sigma = \sqrt{A k g}$ (Atwood number $A$ , wavenumber $k$ , gravity $g$ ). Dense spikes fall, light bubbles rise

Figure 1. RT instability of a dense-over-light interface; linear exp(sigma t) growth saturates into spike-bubble structure. Method: closed-form linear streamfunction + saturating nonlinear advection.

Atwood A0.50

k (modes)3

gravity g1.0

animation speed2

WHAT TO TRY

Raise the Atwood number A: the denser fluid on top sinks faster into the lighter one below, since the growth rate sigma scales with the density contrast. Heavy-over-light is always unstable.
Pick a shorter wavelength (higher k): small ripples grow faster initially, but they soon roll into the classic mushroom spikes and bubbles.
Turn up gravity g: the instability accelerates, the same fingering that shapes supernova remnants and inertial-confinement-fusion implosions.