# Complex lamellar vector field

In vector calculus, a **complex lamellar vector field** is a vector field in three dimensions which is orthogonal to its own curl. That is,

Complex lamellar vector fields are precisely those that are normal to a family of surfaces. A special case are irrotational vector fields, satisfying

An irrotational vector field is locally the gradient of a function, and is therefore orthogonal to the family of level surfaces (the equipotential surfaces). Accordingly, the term **lamellar vector field** is sometimes used as a synonym for an irrotational vector field.[1]
The adjective "lamellar" derives from the noun "lamella", which means a thin layer. The *lamellae* to which "lamellar flow" refers are the surfaces of constant potential, or in the complex case, the surfaces orthogonal to the vector field.

## Notes

- Aris 1989, p. 64

## References

- Aris, Rutherford (1989),
*Vectors, tensors, and the basic equations of fluid mechanics*, Dover, ISBN 0-486-66110-5