3D Vortex Ring Collision

Watch vortex rings interact through the Biot-Savart law. The 1/r singularity in induced velocity is replaced by an imposed soft-core for this illustrative browser model.

Biot-Savart Law

v = (Gamma/4pi) * integral[ dl x r / |r|^3 ]

1/r Singularity

The code's soft-core radius prevents infinite self-induced velocity.

Leapfrogging

Try the Leapfrogging preset to see coaxial rings pass through each other!

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Physics Background

Vortex rings are toroidal structures of concentrated vorticity commonly seen in smoke rings, dolphin bubble rings, and jet engine exhaust. The velocity field induced by a vortex filament follows the Biot-Savart law, which has a 1/r singularity at the filament core.

Imposed Core Regularization

Without regularization, self-induced velocity is infinite. The demo applies:

|r|_eff = sqrt(r^2 + r_core^2)

This bounds the maximum induced velocity
while preserving far-field dynamics.