Vorticity
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| - | \omega | + | \omega \equiv \textrm{curl}(u) \equiv \nabla \times u |
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| - | In tensor notation, vorticity is given by | + | In tensor notation, vorticity is given by: |
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| - | where <math>\epsilon_{ijk}</math> is the [[alternating tensor]]. The components of vorticity in Cartesian coordinates are | + | where <math>\epsilon_{ijk}</math> is the [[alternating tensor]]. The components of vorticity in Cartesian coordinates are;: |
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== Physical Significance == | == Physical Significance == | ||
| + | The vorticity can be seen as a vector having magnitude equal to the maximum "circulation" at each point and to be oriented perpendicularly to this plane of circulation for each point. | ||
== Related Pages == | == Related Pages == | ||
*[[Vorticity transport equation]] | *[[Vorticity transport equation]] | ||
Latest revision as of 10:07, 14 June 2007
Vorticity is a vector field variable which is derived from the velocity vector. Mathematically, it is defined as the curl of the velocity vector
In tensor notation, vorticity is given by:
where 
is the alternating tensor. The components of vorticity in Cartesian coordinates are;:
This can be obtained by using determinants
where 
are the unit vectors for the Cartesian coordinate system.
Physical Significance
The vorticity can be seen as a vector having magnitude equal to the maximum "circulation" at each point and to be oriented perpendicularly to this plane of circulation for each point.
