Examples
In a mass of fluid that is rotating like a rigid body, the vorticity is twice the angular velocity vector of that rotation. This is the case, for example, of water in a tank that has been spinning for a while around its vertical axis, at a constant rate.
The vorticity may be nonzero even when all particles are flowing along straight and parallel pathlines, if there is shear (that is, if the flow speed varies across streamlines). For example, in the laminar flow within a pipe with constant cross section, all particles travel parallel to the axis of the pipe; but faster near that axis, and practically stationary next to the walls. The vorticity will be zero on the axis, and maximum near the walls, where the shear is largest.
Conversely, a flow may have zero vorticity even though its particles travel along curved trajectories. An example is the ideal irrotational vortex, where most particles rotate about some straight axis, with speed inversely proportional to their distances to that axis. A small parcel of fluid that does not straddle the axis will be rotated in one sense but sheared in the opposite sense, in such a way that the their mean angular velocity about their center of mass is zero.
| Example flows: | ||
| Rigid-body-like vortex | Parallel flow with shear | Irrotational vortex |
| Absolute velocities around the highlighted point: | ||
| Relative velocities (magnified) around the highlighted point | ||
| Vorticity ≠ 0 | Vorticity ≠ 0 | Vorticity = 0 |
Another way to visualize vorticity is to imagine that, instantaneously, a tiny part of the fluid becomes solid and the rest of the flow disappears. If that tiny new solid particle would be rotating, rather than just moving with the flow, then there is vorticity in the flow.
Read more about this topic: Vorticity
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