Simple model for drag reduction

Direct numerical simulations established that the finite-extension nonlinear-elasticity-Peterlin (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 paper a simple one-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.