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 [Fx, Fy, Fz].
Expanded, ∇×F looks like:
[∂Fz/∂y - ∂Fy/∂z, ∂Fz/∂x - ∂Fx/∂z, ∂Fy/∂x - ∂Fx/∂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 following determinant:
| 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.