Presets
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Fluids and initial ripple
The growth rate depends on A g k only; try two modes to see competition.
Model checks
The science
Linear instability
With densities ρ1 (light, below) and ρ2 (heavy, above), the Atwood number is A = (ρ2 - ρ1)/(ρ2 + ρ1). A sinusoidal ripple of wavenumber k grows as eσt with σ = √(A g k): short waves grow fastest, and the instability needs no trigger other than a tiny perturbation.
The solver
The Boussinesq vorticity equation ∂ω/∂t + u·∇ω = -2 A g ∂c/∂x (c is the heavy-fluid fraction) is stepped with a semi-Lagrangian scheme; ∇²ψ = -ω is solved by successive over-relaxation with u = ∂ψ/∂y, v = -∂ψ/∂x. The box is periodic sideways with free-slip top and bottom walls.
Honest simplifications: 2D Boussinesq (small density ratios only; at large A the bubble/spike asymmetry is under-estimated), no viscosity, surface tension or compressibility, a 64x64 grid with unavoidable numerical diffusion that smooths the roll-ups and widens the interface slightly (growth rates come out several per cent below the sharp-interface value), and a late-stage mixing layer that is resolution-dependent. Real RT flow is 3D and turbulent.
What to try
- Compare Low contrast (A = 0.1) with Strong acceleration: slow lazy growth against fast mushrooms.
- Press Two competing waves: the longer wave eventually dominates.
- Use Random mixing layer to see a turbulent-looking layer grow.