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. The adjective "lamellar" derives from the noun "lamella", which means a thin layer. In Latin, lamella is the diminutive of lamina (but do not confuse with laminar flow). 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.

References

• Aris, Rutherford (1989), Vectors, tensors, and the basic equations of fluid mechanics, Dover, ISBN 0486661105