linguistic:translation, structural:reformatting
Vorticity

The vorticity ω {\displaystyle {\boldsymbol {\omega }}} of a vector field can be defined by:

The vorticity of an irrotational field is zero everywhere. Kelvin's circulation theorem states that a fluid that is irrotational in an inviscid flow will remain irrotational. This result can be derived from the vorticity transport equation, obtained by taking the curl of the Navier–Stokes equations.

For a two-dimensional field, the vorticity acts as a measure of the local rotation of fluid elements. The vorticity does not imply anything about the global behavior of a fluid. It is possible for a fluid that travels in a straight line to have vorticity, and it is possible for a fluid that moves in a circle to be irrotational.