  A Beltrami field is an eigenvector of the curl operator. Beltrami fields
describe steady flows in fluid dynamics and force free magnetic fields in
plasma turbulence. By application of the Lie-Darboux theorem of differential
geoemtry, we prove a local representation theorem for Beltrami fields. We find
that, locally, a Beltrami field has a standard form amenable to an
Arnold-Beltrami-Childress flow with two of the parameters set to zero.
Furthermore, a Beltrami flow admits two local invariants, a coordinate
representing the physical plane of the flow, and an angular momentum-like
quantity in the direction across the plane. As a consequence of the theorem, we
derive a method to construct Beltrami fields with given proportionality factor.
This method, based on the solution of the eikonal equation, guarantees the
existence of Beltrami fields for any orthogonal coordinate system such that at
least two scale factors are equal. We construct several solenoidal and
non-solenoidal Beltrami fields with both homogeneous and inhomogeneous
proportionality factors.
