In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow. This was first proved by Jean-Jacques Moreau in 1961 and Moffatt derived it in 1969 without the knowledge of Moreau's paper. This helicity invariant is an extension of Woltjer's theorem for magnetic helicity.

Let u ( x , t ) {\displaystyle \mathbf {u} (x,t)} be the velocity field and ∇ × u {\displaystyle \nabla \times \mathbf {u} } the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible ( ∇ ⋅ u = 0 {\displaystyle \nabla \cdot \mathbf {u} =0} ), or it is compressible with a barotropic relation p = p ( ρ ) {\displaystyle p=p(\rho )} between pressure p {\displaystyle p} and density ρ {\displaystyle \rho } ; and (iii) any body forces acting on the fluid are conservative. Under these conditions, any closed surface S {\displaystyle S} on which n ⋅ ( ∇ × u ) = 0 {\displaystyle n\cdot (\nabla \times \mathbf {u} )=0} reference