Vortex Reconnection

Vortex filaments approach, reconnect, change topology — helicity transfer

Biot-Savart law:
u(x) = Γ/4π ∮ dl×r̂/|r|²

Before reconnection:
H = Γ²·Lk (link number)

After reconnection:
Lk → 0 (unlinked loops)
Helicity transferred
to writhe + twist

Kelvin's theorem:
Γ = const along vortex
(inviscid flow)
Viscosity enables
reconnection events
t = 0.00