Viscous Drag Reduction Examined in the Light of a New Model of Wall Turbulence

Abstract

The effect of soluble polymer additives on the structure of wall turbulence is examined in the light of a new theoretical model of wall turbulence, and explained in terms of the ability of the polymer macromolecules to substantially increase the hydrodynamic stability of the viscous sublayer flow. Drag reduction, increase in sublayer thickness and apparent ‘slip’ of the velocity profile, which have been observed experimentally are shown to result directly from increased sublayer stability. Specific examples are presented of the predicted effect of polymer additives on the distributions of mean velocity, turbulent shear stress, turbulence production and longitudinal velocity fluctuations. In particular, it is shown that while turbulence intensity may decrease in dilute polymer solutions, the overall longitudinal velocity fluctuations may be greatly enhanced by increased (non-turbulent) time-dependent activity in the sublayer. It is consequently suggested that considerable caution should be exercised in interpreting ‘turbulence’ measurements in drag-reducing solutions. The effect of surface roughness on wall turbulence and in particular on the flow of dilute polymer solutions is also considered briefly.