Irrotational Flows
The flow velocity of a fluid is a vector field, and the vorticity of the flow can be defined by
A common alternative notation for vorticity is .
If is irrotational, with, then the flow is said to be an irrotational flow. The vorticity of an irrotational flow is zero.
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 flow the vorticity acts as a measure of the local rotation of fluid elements. Note that the vorticity does not imply anything about the global behaviour of a fluid. It is possible for a fluid traveling in a straight line to have vorticity, and it is possible for a fluid which moves in a circle to be irrotational.
Read more about this topic: Conservative Vector Field
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