One field, and the two parts the theorem splits it into

A velocity field made of a smooth source, a smooth vortex and a uniform stream, and the two fields the Helmholtz decomposition returns for it. The first carries the whole divergence and has no curl anywhere; the second carries the whole curl and has no divergence. They are computed by solving two Poisson problems on a grid, with the divergence and the vorticity differenced from the field rather than taken from the expressions that built it. Adding the two back together does not recover the field.

3 essays call field-anatomy. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

It is also the blast radius. Changing field-anatomy changes every figure listed here at once, and on this site it may change what they assert as well as what they show — which is what has to be rebuilt and looked at before the change is believed.