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,

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

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

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

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.