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
Famous quotes containing the word flows:
“It is a mischievous notion that we are come late into nature; that the world was finished a long time ago. As the world was plastic and fluid in the hands of God, so it is ever to so much of his attributes as we bring to it. To ignorance and sin, it is flint. They adapt to themselves to it as they may; but in proportion as a man has anything in him divine, the firmament flows before him and takes his signet and form.”
—Ralph Waldo Emerson (1803–1882)