Two vortex rings approach, reconnect, and change topology — a fundamental mechanism in turbulence and superfluid helium. The Biot-Savart law governs filament velocity: u(x) = (Γ/4π) ∮ (ds×r)/|r|³, regularized with vortex core size a.
Configuration
Status: approaching...
u(x) = Γ/4π ∮ (dl×r̂)/r²
Core reg: r² → r²+a²
Reconnection: topology switch
when filaments cross within ~a
Helicity H = ∫u·ω dV conserved
before reconnection