Kelvin-Helmholtz Instability
Shear flow at a fluid interface — vortex rollup and mixing
Flow Parameters
Velocity shear ΔU:
2.0
Density ratio ρ₂/ρ₁:
1.0
Surface tension σ:
0.0
Perturbation amp:
0.05
Wavenumber k:
2
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Stability
Growth rate σ_r
—
KH criterion
—
Richardson Ri
—
Time
0
Theory
σ = k|ΔU|√(ρ₁ρ₂)/(ρ₁+ρ₂)
Stable if: k σ_T > g(ρ₁−ρ₂)|ΔU|²
Ri = gΔρ/ρ(dU/dz)⁻² < ¼
Rollup time ~ 1/σ_r