A rotational vortex – a vortex that rotates in the same way as a rigid body – cannot exist indefinitely in that state except through the application of some extra force, that is not generated by the fluid motion itself. It has non-zero vorticity everywhere outside the core. Rotational vortices are also called rigid-body vortices or forced vortices.
For example, if a water bucket is spun at constant angular speed  about its vertical axis, the water will eventually rotate in rigid-body fashion. The particles will then move along circles, with velocity  equal to . In that case, the free surface of the water will assume a parabolic shape.
In this situation, the rigid rotating enclosure provides an extra force, namely an extra pressure gradient in the water, directed inwards, that prevents transition of the rigid-body flow to the irrotational state.