  The phenomenon of drag reduction by polymer additives had been studied in
simulations on the basis of non-Newtonian fluid mechanical models that take
into account the field of polymer extension (conformation tensor) and its
interaction with the velocity field. Drag reduction was found in both
homogeneous and wall bounded turbulent flows. In the latter case it was shown
recently that the notion of scale-dependent effective viscosity allows
quantitative predictions of the characteristics of drag reduction in close
correspondence with experiments. In this paper we demonstrate that also drag
reduction in homogeneous turbulence is usefully discussed in terms of a
scale-dependent viscosity. In other words, the essence of the phenomena under
study can be recaptured by an "equivalent" equation of motion for the velocity
field alone, with a judiciously chosen scale-dependent effective viscosity that
succinctly summarizes the important aspects of the interaction between the
polymer conformation tensor field and the velocity field. We will also clarify
here the differences between drag reduction in homogeneous and wall bounded
flows.
