Variational approach to a turbulent swirling pipe flow with the aid of helicity

A turbulent swirling flow in a circular pipe is studied with the aid of a variational method. A prominent feature of the flow is the occurrence of a retarded or reversed mean-flow profile near the central axis. Diffusion effect is generally enhanced in a turbulent flow. A mechanism under which these two properties coexist is sought with resort to a variational approach combined with helicity. The mean-flow field is expressed by the mean vorticity proportional to its curl. On this basis, the centerline axial vorticity is shown to play a central role in the occurrence of axial-velocity retardation or reversal in a turbulent swirling pipe flow. Suggestions on modeling the Reynolds stress are obtained from the mean-vorticity equation.