From AMS Glossary
A vertically oriented vortex with a width perpendicular to the axis of rotation of between 40 m and 4 km.
It is often used to refer to a small, vertically oriented closed cyclonic circulation that is either 1) embedded within a convective storm, or 2) a near-surface vortex along a horizontal convergence line.
Fujita, T. T., 1981. Tornadoes and Downbursts in the Context of Generalized Planetary Scales. J. Atmos. Sci., 38. 1511–1534, doi:10.1175/1520-0469(1981)038<1511:TADITC>2.0.CO;2.