Plumera

Plumera holds heavy fluid above light, and gravity pulls it into fingers: spikes fall, bubbles rise.

The Physics

When a heavy fluid sits on top of a light one in gravity, any ripple on the interface grows. In the linear theory, a ripple of wavenumber k grows exponentially at rate σ, depending on the density contrast through the Atwood number. Spikes of heavy fluid fall and bubbles of light fluid rise.

σ = √(A g k), A = (ρ_h − ρ_l)/(ρ_h + ρ_l)

• σ: growth rate (1/s)
• A: Atwood number (dimensionless)
• g: gravitational acceleration (m/s²)
• k: wavenumber (1/m)
• ρ_h, ρ_l: heavy and light densities (kg/m³)

Lord Rayleigh analysed it in 1882, and G. I. Taylor followed in 1950.

Honest caveat: The formula ignores viscosity and surface tension.

On the shirt

Front: Plumera, the pixel-art character, with the title. Back: the growth rate, the Atwood number, spikes and bubbles and the 1882 and 1950 sources. Printed on a unisex tee.