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Maximum drag reduction asymptotes and the cross-over to the Newtonian plug. (English) Zbl 1085.76004
Summary: We employ the full FENE-P model of the hydrodynamics of a dilute polymer solution to derive a theoretical approach to drag reduction in wall-bounded turbulence. We recapture the results of a recent simplified theory [V. S. L’vov et al., Phys. Rev. Lett. 70, 026304 (2004)] 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 of viscoelastic turbulence in a channel.

76A10 Viscoelastic fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76F70 Control of turbulent flows
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