Parameters
Instability
Growth rate σ: —
Atwood At: —
Stability? —
Interface amp: —
Time: 0
Phase vφ: —
Theory
Kelvin-Helmholtz:
Vortex sheet at ρ₁/ρ₂ shear interface.
Dispersion relation:
Unstable for all k (incompressible).
Growth ~ e^{σt}
Nonlinear: interface rolls up into cat's-eye vortices; eventually breaks into turbulence. Seen at cloud boundaries, ocean-atmosphere interface, astrophysical jets.
Vortex sheet at ρ₁/ρ₂ shear interface.
Dispersion relation:
σ = k|ΔU|/2 · √(1−At²)
where At=(ρ₁−ρ₂)/(ρ₁+ρ₂)Unstable for all k (incompressible).
Growth ~ e^{σt}
Nonlinear: interface rolls up into cat's-eye vortices; eventually breaks into turbulence. Seen at cloud boundaries, ocean-atmosphere interface, astrophysical jets.