Curl

A vector operator that shows a vector field's tendancy to rotate about a point. Common examples include:

• In a tornado the winds are rotating about the eye, and a vector field showing wind velocities would have a non-zero curl at the eye, and possibly elsewhere.
• In a vector field that describes the linear velocities of each individual part of a rotating disk, the curl will have a constant value on all parts of the disk.
• If a freeway was described with a vector field, and the lanes had different speed limits, the curl on the borders between lanes would be non-zero.

In mathematics the curl is noted by:

∇×F

Where F is the vector field the curl is being applied to, and is composed of [F_x, F_y, F_z].

Expanded, ∇×F looks like:

[∂F_z/∂y - ∂F_y/∂z, ∂F_z/∂x - ∂F_x/∂z, ∂F_y/∂x - ∂F_x/∂y]

A simple way to remember the expanded form of the curl is to think of it as:

[∂/∂x, ∂/∂y, ∂/∂z]×F

or as the determinant of the following matrix:

i	j	k
∂/∂x	∂/∂y	∂/∂z
Fx	Fy	Fz

where i, j, and k are the unit vectors for the x, y, and z axes, respectively.

Note that the result of the curl operator is not really a vector, it is a pseudovector?. This means that it takes on opposite values in left-handed and right-handed coordiante systems.