  We employ the full FENE-P model of hydrodynamics of a dilute polymer
solutions to derive a theoretical approach to drag reduction in wall bounded
turbulence. We recapture the results of a recent simplified theory which
derived the universal Maximum Drag Reduction (MDR) asymptote, and complement
that theory with a discussion of the cross-over from the MDR to the Newtonian
plug when the drag reduction saturates. The FENE-P model gives rise to a rather
complex theory due to the interaction of the velocity field with the polymeric
conformation tensor, making analytic estimates quite taxing. To overcome this
we develop the theory in a computer-assisted manner, checking at each point the
analytic estimates by Direct Numerical Simulations (DNS) of viscoelastic
turbulence in a channel.
