Curl and Divergence of Vector Fields

Curl and divergence describe two fundamental ways a vector field can behave. A vector field assigns both magnitude and direction to each point in space, such as the velocity of water flowing in a river. Leaves floating on the surface may reveal regions where the water swirls and other regions where it spreads outward or gathers inward. These mot...

Imagine leaves floating on a river. Some areas swirl like small whirlpools, while other areas spread apart. These two distinct motions are the fundamental behaviors of any vector field.

These two behaviors are known as curl and divergence, respectively.

Curl measures how much a vector field rotates around a point. Mathematically, it ...