The purpose of this project was to develop a second order model for weakly swirling flows. The model was based on a successful model for the buoyancy driven mixed layer of the atmosphere. Swirling flows present a challenge to the modeler due to the influence of radial turbulent transport on the radial distribution of azimuthal velocity. This is weakly analogous to the effect of density stratification in a flow with gravity. A radial distribution of angular momentum increasing outward will have a stabilizing influence, and will suppress radial transport and reduce the rate of spread of a scalar marker, while a radial distribution of angular momentum decreasing outward will have the opposite effect.