A vortex filament is the ideal thin-core limit of a vortex tube, concentrating a finite circulation on a curve. In an unbounded incompressible fluid with velocity tending to zero at infinity, its induced velocity field follows the vorticity version of the Biot-Savart law. The ideal field is singular on the filament; finite-core models are needed there. A closed circular filament is a thin vortex ring.
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