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

R. Benzi·E. De Angelis·I. Procaccia·V. S. L'vov·V. Tiberkevich
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Abstract

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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R. Benzi, E. De Angelis, I. Procaccia, V. S. L'vov, V. Tiberkevich. 2004-05-13. Maximum Drag Reduction Asymptotes and the Cross-Over to the Newtonian Plug. https://arxiv.org/abs/nlin/0405033

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