An infrared method for viscous fluids. I. Point vortices and vortex sheets in two dimensions

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Abstract
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.

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