Knotted vortex filaments; helicity H = ∫v·ω dV is a topological invariant
Vortex filaments in ideal fluid are governed by Biot-Savart: v(r) = (Γ/4π)∮(dl×r̂)/r². The helicity H = ∫v·ω dV counts the linking number of vortex lines and is conserved in Euler flow. The trefoil knot has self-linking SL = 3; topological reconnection changes helicity, requiring viscosity.