Winding Number & Vortices

Topological vortices in 2D phase fields — click to place vortices, watch winding numbers and annihilation

Total winding number:
0
Vortices: 0

Winding number:
n = (1/2π) ∮ dθ

Topological charge is conserved — vortices only annihilate in pairs of opposite charge
Click canvas to place vortex.

Colors show phase angle θ(x,y) ∈ [0,2π):
θ=0 θ=π/2 θ=π θ=3π/2