Fluid Dynamics & Vorticity

Kelvin-Helmholtz Instability

Simulate Lord Kelvin and Hermann von Helmholtz's fluid shear instability. Velocity differences $\Delta U = U_1 - U_2$ across a fluid interface cause vortex sheet rolling into characteristic spiral ocean billows when Richardson number $\text{Ri} < 0.25$.

Velocity Shear ΔU 4.0 m/s

Richardson Number Ri 0.08 (UNSTABLE)

Max Vorticity ω_max 12.4 s⁻¹

Shear Flow Controls

Upper Layer Speed U₁ 2.0 m/s

Lower Layer Speed U₂ -2.0 m/s

Visual Overlay

Show Spiral Vortex Billow Rolls

Show Velocity Shear Vectors

Show Fluid Layer Badges

Controls

Kelvin-Helmholtz Instability & Richardson Number

Richardson Number: Ri = - (g / ρ) · [ (∂ρ/∂z) / (∂u/∂z)² ]
Stability Criterion: Ri < 0.25 ⇒ Shear Instability Grows!
Linear Growth Rate: σ = k · (|U₁ - U₂| / 2)

Developer Reference

Core Algorithm & Standalone Script

// Kelvin-Helmholtz shear vortex billow roll solver
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// Ri = -(g / rho) * (d_rho / dz) / (du / dz)^2