A Unified View of Topological Invariants of Fluid Flows

The helicity is a topological invariant of an ideal fluid in three function of vorticity as topological invariants. This is extended to axisymmetric flows. We show that these are variants of the cross helicity. Noether's theorem associated with the particle relabeling symmetry underpins this unified view. A comment is given to the bearing of Kelvin's circulation theorem with Noether's second theorem.