Vortex Ring Cross-Section Simulator (2D)

This 2D companion to the 3D smoke-ring simulation slices a vortex ring in half and shows the mechanism that actually drives it: two counter-rotating vortex cores whose mutual induction pushes the pair steadily forward, following Kelvin's vortex-ring theory. Drag the circulation slider to change how strongly each core spins, drag the ring-radius slider to change how far apart the cores sit, and watch the propagation speed, live ring radius, and circulation readouts update in real time as smoke tracer particles swirl around each core and drift downstream with the pair. Raise the core viscosity to watch a real physical effect play out — the ring's core spreads, its effective radius grows, and its forward speed decays, just as a real smoke ring slows and swells before dissipating.