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 v ariational method. A prominent feature of the flow is the occurrence of a r etarded or reversed mean-flow profile near the central axis. Diffusion effe ct is generally enhanced in a turbulent flow. A mechanism under which these two properties coexist is sought with resort to a variational approach com bined 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 retardati on or reversal in a turbulent swirling pipe flow. Suggestions on modeling t he Reynolds stress are obtained from the mean-vorticity equation. (C) 2001 American Institute of Physics.