The Reduced Drag of Polymer Solutions in Turbulent and Transient Laminar Shear Flows

The laminar flow of a polymer solution near a flat plate of infinite extent is investigated theoretically for three cases: (a) the plate is impulsively started and moves in its own plane with a constant velocity; (b) it executes linear harmonic oscillations in its own plane; (c) its motion in this plane is a random function of time. In each case the mean square value of the drag exerted on the plate by the polymer solution is predicted to be less than that by a Newtonian fluid of the same viscosity and density. The results are combined with a simple model for the turbulent boundary layer, and a number of experimentally observed characteristics of the turbulent flow drag reduction phenomenon are predicted. The merits of this transient shear explanation for the unusual behavior of polymer solutions in turbulent flow are compared to those of previously offered hypotheses.