A method of extracting the behavior of velocity/vorticity fields caused by the low‐frequency, or infrared (IR), portion of nonlinear interactions in arbitrary spatial dimensions is transcribed from the Schwinger/Fradkin representation of Green’s functions in quantum field theory to problems of viscous Navier–Stokes fluids. The general IR formalism is developed and applied to certain simple, two‐dimensional situations involving point vortices and vortex sheets. As an illustration point vortices inserted into a viscous fluid are shown to perform a finite number of revolutions about each other before they dissipate and disappear.