Hamiltonian Point Vortex Dynamics in 2D

N point vortices in 2D are a Hamiltonian system with H = −(1/4π)Σᵢ<ⱼ ΓᵢΓⱼ ln|rᵢ−rⱼ|. Two vortices orbit each other periodically (integrable); three vortices can be chaotic. Vortex color encodes circulation sign (red=positive, blue=negative).