  Direct Numerical Simulations established that the FENE-P model of
viscoelastic flows exhibits the phenomenon of turbulent drag reduction which is
caused in experiments by dilute polymeric additives. To gain analytic
understanding of the phenomenon we introduce in this Letter a simple
1-dimensional model of the FENE-P equations. We demonstrate drag reduction in
the simple model, and explain analytically the main observations which include
(i) reduction of velocity gradients for fixed throughput and (ii) increase of
throughput for fixed dissipation.
