Maximum Drag Reduction Asymptotes and the Cross-Over to the Newtonian Plug

Details Maximum Drag Reduction Asymptotes and the Cross-Over to the Newtonian Plug Maximum Drag Reduction Asymptotes and the Cross-Over to the Newtonian Plug

2004-05-13

arxiv.org/abs/nlin/0405033v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 6 figures. submitted to J. Fluid. Mech

Scientific paper

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.

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