Vorticity — Leapfrogging Vortices Two spinning vortex pairs chase each other down a line, dragging a hundred thousand tracer particles with them. The trailing pair is squeezed narrow by the leader’s swirl, speeds up, and darts through the middle; the leader spreads and slows. Then they trade places, over and over — the flat version of two smoke rings. The journey: Helmholtz’s laws (1858): a vortex is carried bodily by the fluid and never lets go of its neighbours. Model each pair as two ideal point vortices; every particle just drifts in the summed swirl (Biot–Savart).