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A vector operation upon a vector field which represents the rotation of the field, related to the circulation of the field at each point. The curl is invariant with respect to coordinate transformations and is usually written "curl F" of " Missing Image:IMG src="c_files/del.gif" * F" where Missing Image:IMG src="c_files/del.gif" is the del-operator. In Cartesian coordinates, if F has the components Fx, Fy, Fz the curl is

Missing Image:IMG height=49 src="c_files/72curl.gif" width=322

in other coordinate systems may be found in any text on vector analysis.
The curl of a two-dimensional vector field is always in a field of solid rotation it is equal to twice the angular velocity. Occasionally the vorticity is defined as one-half the curl.
The curl of a two dimensional vector field is always normal to the vectors of the field; this is not necessarily true in three dimensions. Compare divergence.


This article is based on NASA's Dictionary of Technical Terms for Aerospace Use