A divergenceless field, also called a Solenoidal Field, is a Field for which . Therefore, there exists a such that . Furthermore, can be written as
(1)
where
(2)
(3)
Following Lamb, and are called Toroidal Field and Poloidal Field.See also Beltrami Field, Irrotational Field, Poloidal Field, Solenoidal Field, Toroidal Field