From AMS Glossary
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A condensation cloud, typically funnel-shaped and extending outward from a cumuliform cloud, associated with a rotating column of air (a vortex) that may or may not be in contact with the surface. If the rotation is violent and in contact with the surface, the vortex is a tornado.
Funnel clouds can occur through a variety of processes in association with convection. For example, small funnel clouds are infrequently seen extending from small, dissipating cumulus clouds in environments with significant vertical wind shear in the cloud-bearing layer.
Bluestein, H. 1994. High-based funnel clouds in the Southern Plains. Mon. Wea. Rev.. 122. 2631–2638.