The curl of a field is formally defined as the circulation density at each point of the field. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields.

Nov 16, 2022 · In this section we will introduce the concepts of the curl and the divergence of a vector field. We will also give two vector forms of Green’s Theorem and show how the curl can be used to …

Dec 11, 2025 · In this section, we examine two important operations on a vector field: divergence and curl. They are important to the field of calculus for several reasons, including the use of curl and …

Oct 25, 2025 · Curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional space. In other words, it measures the tendency of the field to rotate around a point.

As we saw earlier in this section, the vector output of curl (F) represents the rotational strength of the vector field F as a linear combination of rotational strengths (or circulation densities) from two …

To see what curl is measuring globally, imagine dropping a leaf into the fluid. As the leaf moves along with the fluid flow, the curl measures the tendency of the leaf to rotate. If the curl is zero, then the leaf …

If a fluid flows in three-dimensional space along a vector field, the rotation of that fluid around each point, represented as a vector, is given by the curl of the original vector field evaluated at that point.

The reason for the name curl is that if a particle has curl ⃗F = ⃗0, then, in a fluid, that particle will not rotate; if curl ⃗F 6= ⃗0, then the particle will rotate, like in a whirlpool or an eddy.

This is an important quantity in the description not only of fluid flow but also electro-magnetic fields, and it is related to whether the vector field is conservative.

Intuitive introduction to the curl of a vector field. Interactive graphics illustrate basic concepts.