J. Fluid Mech. (2004), vol. 514, pp. 271–280. c  2004 Cambridge University Press DOI: 10.1017/S0022112004000291 Printed in the United Kingdom 271 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows By YVES DUBIEF 1 , CHRISTOPHER M. WHITE 2 , VINCENT E. TERRAPON 2 , ERIC S. G. SHAQFEH 2,3 , PARVIZ MOIN 1,2 AND SANJIVA K. LELE 2,4 1 Center for Turbulence Research, 2 Mechanical Engineering Department, 3 Department of Chemical Engineering, 4 Department of Aeronautics and Astronautics, Stanford University, CA 94305, USA (Received 15 December 2003 and in revised form 2 June 2004) Numerical simulations of turbulent polymer solutions using the FENE-P model are used to characterize the action of polymers on turbulence in drag-reduced flows. The energetics of turbulence is investigated by correlating the work done by polymers on the flow with turbulent structures. Polymers are found to store and to release energy to the flow in a well-organized manner. The storage of energy occurs around near-wall vortices as has been anticipated for a long time. Quite unexpectedly, coherent release of energy is observed in the very near-wall region. Large fluctuations of polymer work are shown to re-energize decaying streamwise velocity fluctuations in high- speed streaks just above the viscous sublayer. These distinct behaviours are used to propose an autonomous regeneration cycle of polymer wall turbulence, in the spirit of Jim´ enez & Pinelli (1999). 1. Introduction The addition of small amounts of long-chain polymer molecules to wall-bounded flows can lead to dramatic drag reduction. Although this phenomenon has been known for about fifty years, the action of the polymers and its effect on turbulent structures are still unclear. Detailed experiments have characterized two distinct regimes (Warholic, Massah & Hanratty 1999), referred to as low drag reduction (LDR) and high drag reduction (HDR). The first regime exhibits similar statistical trends to Newtonian flow: the log-law region of the mean velocity profile remains parallel to that of the Newtonian flow but its lower bound moves away from the wall and the upward shift of the log-region is a function of drag reduction, herein referred to as DR. Although streamwise fluctuations are increased and transverse ones are reduced, the shape of the r.m.s. velocity profiles is similar. At higher drag reductions, larger than about 40%, the flow enters the HDR regime for which the slope of the log-law is dramatically augmented and the Reynolds shear stress is small (Warholic et al. 1999; Ptasinski et al. 2003). The drag reduction is eventually bounded by a maximum drag reduction (MDR, Virk & Mickley 1970) which is a function of the Reynolds number. In drag-reduced flows, a stress deficit is observed in the stress balance whose large magnitude at HDR has been interpreted as the necessary input of energy from the polymers to the flow for the sustenance of the asymptotic MDR turbulence (Warholic et al. 1999). Recently, numerical simulations have allowed the simultaneous study of velocity and polymer fields, giving the opportunity to relate turbulence and polymer