Evolution of helicity in fluid flows

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=2 lambda omega center dot zeta and the moving boundary surfaces of the fluid. Here, omega and zeta are the vorticity and swirl components of the vortex field {omega,zeta} and lambda is a constitutive or material parameter of the fluid. Our first result using the vector calculus identifies the scalar helicity as h(t)=A omega. This result is then generalized using the calculus of differential forms, yielding other results including the existence of a helicity current vector proportional to (phi omega-lambda Ax zeta).