In theory, the speed  of the particles (and, therefore, the vorticity) in a vortex may vary with the distance  from the axis in many ways.  There are two important special cases, however:
* If the fluid rotates like a rigid body – that is, if the angular rotational velocity  is uniform, so that  increases proportionally to the distance  from the axis – a tiny ball carried by the flow would also rotate about its center as if it were part of that rigid body.  In such a flow, the vorticity is the same everywhere: its direction is parallel to the rotation axis, and its magnitude is equal to twice the uniform angular velocity  of the fluid around the center of rotation.
* If the particle speed  is inversely proportional to the distance  from the axis, then the imaginary test ball would not rotate over itself; it would maintain the same orientation while moving in a circle around the vortex axis. In this case the vorticity  is zero at any point not on that axis, and the flow is said to be irrotational.