Kelvin-Helmholtz Instability
Shear flow instability & vortex roll-up at fluid interface
Flow Parameters
Shear velocity ΔU:
1.00
Density ratio ρ₂/ρ₁:
1.00
Perturbation amplitude:
0.02
Mode number k:
3
Viscosity ν:
0.001
Pause
Restart
KH instability
occurs at the interface between fluids with different velocities.
Growth rate:
σ = k|ΔU|/2 · √(1 - At²)
At = (ρ₂-ρ₁)/(ρ₂+ρ₁) Atwood #
Critical wavelength:
λ_c = 2πg(ρ₂²-ρ₁²)/(k²ρ₁ρ₂ΔU²)
Heavier upper fluid adds stabilizing gravity (Rayleigh-Taylor coupling).