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The science
Each vortex is a Lamb-Oseen vortex, the exact viscous solution of a point vortex that spreads: v_theta(r,t) = Gamma/(2 pi r) * (1 - exp(-r^2 / r_c^2)) with r_c^2 = r_0^2 + 4 nu t. The vorticity is omega = Gamma/(pi r_c^2) * exp(-r^2/r_c^2).
Every vortex and tracer is advected by the background flow U plus the velocity induced by the other vortex (Biot-Savart in 2D). Two equal vortices co-rotate at angular rate Omega = 2 Gamma / (2 pi d^2) = Gamma/(pi d^2); opposite vortices form a dipole that translates at V = Gamma/(2 pi d). When the core radius grows so that d < ~3.3 r_c the same-sign pair merges (critical merger distance, Meunier et al. 2005); this app marks the merger but does not model the merged filament exactly.
Simplifications: 2D only (no vortex stretching), cores stay Gaussian (no deformation), tracers are passive and do not feed back on the flow. Boundaries are open.
What to try
- Preset Dipole: the pair drives straight ahead; compare measured speed with the check.
- Raise viscosity: the cores spread and peak vorticity drops as 1/r_c^2.
- Preset Merger: reduce the separation until the pair merges.
- Add background flow and watch both vortices drift together.