Kelvin-Helmholtz Instability 2D — Vortex Sheet Roll-Up

🌀 Kelvin-Helmholtz (2D)

A real periodic vortex sheet: N point vortices on the interface, evolved with the Biot-Savart law and Krasny regularisation — the same discrete method described for the 3D version, run directly here.

Parameters

Velocity difference Δv 2.0 Density ratio ρ₂/ρ₁ 1.0 Perturbation ε 0.05 Regularisation δ (Krasny) 0.30

Diagnostics

Growth rate σ

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Richardson Ri

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Amplitude A

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Billows

Method

N=96 vortex points sit on a periodic interface of circulation Γ = Δv·L/N. Their mutual velocity is the exact periodic Biot-Savart sum (coth kernel) with Krasny desingularisation δ to keep the sheet from tangling. A buoyancy restoring term derived from the Richardson number (Ri < 0.25 unstable) damps growth when the layers are strongly stratified — drag the sliders and watch the billows roll up in real time.