Abstract
An invariant helicity integral and a differential helicity evolution equation are found for viscous fluid flows. A geometrodynamical approach is used, which includes a vortex field. The vortex field is derivable from a vector potential A. The vector potential is then used to characterize the evolution of flow topology. The source of the helicity is found to be the topological parity k=2λω⋅ζ and the moving boundary surfaces of the fluid. Here, ω and ζ are the vorticity and swirl components of the vortex field {ω,ζ} and λ is a constitutive or material parameter of the fluid. Our first result using the vector calculus identifies the scalar helicity as ht=Aω. This result is then generalized using the calculus of differential forms, yielding other results including the existence of a helicity current vector proportional to (ϕω−λA×ζ).
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