  We study the motion of a single helical vortex in an unbounded, inviscid,
incompressible fluid. The vortex is an infinite tube whose centerline is a
helix and whose cross section is a circle of small radius (compared to the
radius of curvature) where the vorticity is uniform and parallel to the
centerline. Ever since Joukowsky (1912) deduced that this vortex translates and
rotates steadily without change of form, numerous attempts have been made to
compute these self-induced velocities. Here we use Hardin's (1982) solution for
the velocity field to find new expressions for the vortex's linear and angular
velocities. Our results, verified by numerically computing the Helmholtz
integral and the Rosenhead-Moore approximation to the Biot-Savart law, are more
accurate than previous results over the whole range of values of the vortex
pitch and cross-section. We then use the new formulas to study the advection of
passive particles near the vortex; we find that the vortex's motion and
capacity to transport fluid depend on its pitch and cross section as follows: a
thin vortex of small pitch moves fast and carries a small amount of fluid; a
thick vortex of small pitch moves at intermediate velocities and is a moderate
carrier itself but it pushes fluid forward along the helix axis; and a vortex
of large pitch, whether thin or thick, moves slowly and carries a large amount
of fluid.
