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,

$\mathbf{F}\cdot (\nabla\times \mathbf{F}) = 0.$

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

$\nabla\times\mathbf{F}=\mathbf{0}.$

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.

See also

• Beltrami vector field
• Conservative vector field

Notes

1. Aris 1989, p. 64

References

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