Kelvin-Helmholtz Instability — Fluid Shear Simulation

🌊 Kelvin-Helmholtz Instability

Two fluid layers moving in opposite directions. The interface rolls up into characteristic billows — seen in clouds, the ocean, Jupiter's bands, and solar corona.

🎛 Parameters

Velocity difference Δv 2.0 Density ratio ρ₂/ρ₁ 1.0 Perturbation ε 0.05 Gravity / stratification g 0.0

📐 Diagnostics

Growth rate σ

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Richardson Ri

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Amplitude A

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Billows

ℹ️ Physics

The Kelvin-Helmholtz instability occurs at the interface of two fluids with a relative velocity. Pressure variations across the boundary amplify perturbations. Growth rate: σ = k·Δv/2 (equal densities). Gravity stabilises via the Richardson number Ri = g·Δρ·L / (ρ·Δv²). Instability requires Ri < 0.25. The simulation uses N=80 vortex points on the interface with Biot-Savart interactions and Krasny regularisation (δ=0.3) to prevent singularities.