A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics,
and in particular in dynamo theory and helioseismology. The toroidal field is defined
as
which can additionally be multiplied by a radial weighting function .
This is equivalent to the definition
where
is a scalar function and the gradient is taken in spherical coordinates.
.
is a scalar function and the gradient is taken in spherical coordinates.
