The problem of fluid dynamics can be greatly simplified if, for every point in space, the strain-rate tensor is diagonalized. This tensor is introduced into the Navier-Stokes equations via material law and divergence of the stress tensor. This article shows that local SO(3)xU(1) gauge fields can be used to locally diagonalize the diffusion components of the strain-rate tensor. The gauge fields resulting from the connection can be interpreted as convection components of the flow, they show properties of quasiparticles and can be interpreted as elementary vortices. Thus, the proposed approach not only offers new insights for the solution and situative simplification of the Navier-Stokes equations, it also uncovers hidden symmetries within the flow convection, allowing - depending on boundary conditions - further interpretation.