Curl is a vector operator which describes the "rotation" of a vector field in three-dimensional Euclidean space. The curl at a point in a field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation.

The curl of a field is denoted as or . The curl of a field is defined as follows

Where , and are the , , and components of respectively, and is treated as the partial derivative operator.

This equation expands out to

Physical Interpretation

If we consider a vector field to represent the velocity of some fluid the divergence represents how much fluid "swirl" around a point.