Vortex Reconnection & Helicity

Helicity H = ∫u·ω dV
Writhe (self-linking)
Twist
ΔH (reconnection)
Helicity: H = ∫ u·ω dV = Γ²·Lk where Lk = Wr + Tw (Calugareanu-White-Fuller).

Reconnection: Vortex tubes approach, anti-parallel segments annihilate, topology changes. H changes by ΔH = ±2Γ².

Moffatt-Ricca (1992): Total helicity conserved in ideal fluid, but redistributes between writhe and twist during reconnection. Non-ideal: helicity cascade to small scales.