  The interaction of polymers with turbulent shear flows is examined. We focus
on the structure of the elastic stress tensor, which is proportional to the
polymer conformation tensor. We examine this object in turbulent flows of
increasing complexity. First is isotropic turbulence, then anisotropic (but
homogenous) shear turbulence and finally wall bounded turbulence. The main
result of this paper is that for all these flows the polymer stress tensor
attains a universal structure in the limit of large Deborah number $\De\gg 1$.
We present analytic results for the suppression of the coil-stretch transition
at large Deborah numbers. Above the transition the turbulent velocity
fluctuations are strongly correlated with the polymer's elongation: there
appear high-quality "hydro-elastic" waves in which turbulent kinetic energy
turns into polymer potential energy and vice versa. These waves determine the
trace of the elastic stress tensor but practically do not modify its universal
structure. We demonstrate that the influence of the polymers on the balance of
energy and momentum can be accurately described by an effective polymer
viscosity that is proportional to to the cross-stream component of the elastic
stress tensor. This component is smaller than the stream-wise component by a
factor proportional to $\De ^2 $. Finally we tie our results to wall bounded
turbulence and clarify some puzzling facts observed in the problem of drag
reduction by polymers.
