Editing Vorticity (section)

==Examples==
In a mass of continuum that is rotating like a rigid body, the vorticity is twice the [[angular velocity]] vector of that rotation. This is the case, for example, in the central core of a [[Rankine vortex]].<ref>Acheson (1990), p. 15</ref>

The vorticity may be nonzero even when all particles are flowing along straight and parallel [[pathline]]s, if there is [[shear (fluid)|shear]] (that is, if the flow speed varies across [[Streamlines, streaklines, and pathlines|streamlines]]). For example, in the [[laminar flow]] within a pipe with constant [[cross section (geometry)|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 [[vortex|irrotational vortex]], where most particles rotate about some straight axis, with speed inversely proportional to their distances to that axis. A small parcel of continuum that does not straddle the axis will be rotated in one sense but sheared in the opposite sense, in such a way that their mean angular velocity ''about their center of mass'' is zero.

:{| border="0"
|-
| style="text-align:center;" colspan=3 | Example flows:
|-
| valign="top" | [[File:Vorticity Figure 01 a-m.gif]]
| valign="top" | [[File:Vorticity Figure 03 a-m.gif]]
| valign="top" | [[File:Vorticity Figure 02 a-m.gif]]
|-
| style="text-align:center;" | Rigid-body-like vortex<br />{{math|''v'' ∝ ''r''}}
| style="text-align:center;" | Parallel flow with shear
| style="text-align:center;" | Irrotational vortex<br />{{math|''v'' ∝ {{sfrac|1|''r''}}}}
|-
| style="text-align:center;" colspan=3 | where {{mvar|v}} is the velocity of the flow, {{mvar|r}} is the distance to the center of the vortex and ∝ indicates [[proportionality (mathematics)|proportionality]].<br />Absolute velocities around the highlighted point:
|-
| valign="top" | [[File:Vorticity Figure 01 b.png]]
| valign="top" | [[File:Vorticity Figure 03 b.png]]
| valign="top" | [[File:Vorticity Figure 02 b.png]]
|-
| style="text-align:center;" colspan=3 | Relative velocities (magnified) around the highlighted point
|-
| valign="top" | [[File:Vorticity Figure 01 c.png]]
| valign="top" | [[File:Vorticity Figure 03 c.png]]
| valign="top" | [[File:Vorticity Figure 02 c.png]]
|-
| style="text-align:center;" | Vorticity ≠ 0
| style="text-align:center;" | Vorticity ≠ 0
| style="text-align:center;" | Vorticity = 0
|}

Another way to visualize vorticity is to imagine that, instantaneously, a tiny part of the continuum becomes solid and the rest of the flow disappears. If that tiny new solid particle is rotating, rather than just moving with the flow, then there is vorticity in the flow. In the figure below, the left subfigure demonstrates no vorticity, and the right subfigure demonstrates existence of vorticity.

:[[File:Illustration of vorticity.svg]]