The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.

SUMMARYAn e cient numerical method to solve the unsteady incompressible Navier-Stokes equations is developed. A fully implicit time advancement is employed to avoid the Courant-Friedrichs-Lewy restriction, where the Crank-Nicolson discretization is used for both the di usion and convection terms. Based on a block LU decomposition, velocity-pressure decoupling is achieved in conjunction with the approximate factorization. The main emphasis is placed on the additional decoupling of the intermediate velocity components with only nth time step velocity. The temporal second-order accuracy is preserved with the approximate factorization without any modiÿcation of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced signiÿcantly. The present decoupling method is validated by solving several test cases, in particular, the turbulent minimal channel ow unit.

It has been known for over six decades that the dissolution of minute amounts of high molecular weight polymers in wall-bounded turbulent flows results in a dramatic reduction in turbulent skin friction by up to 70%. First principles simulations of turbulent flow of model polymer solutions can predict the drag reduction (DR) phenomenon. However, the essential dynamical interactions between the coherent structures present in turbulent flows and polymer conformation field that lead to DR are poorly understood. We examine this connection via dynamical simulations that track the evolution of hairpin vortices, i.e., counter-rotating pairs of quasistreamwise vortices whose nonlinear autogeneration and growth, decay and breakup are centrally important to turbulence stress production. The results show that the autogeneration of new vortices is suppressed by the polymer stresses, thereby decreasing the turbulent drag.

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We examine the autogeneration process by which new hairpin vortices are created from a sufficiently strong hairpin vortex, leading to the formation of a hairpin packet. Emphasis is placed on the effects of background noise on packet formation. The initial conditions are given by conditionally averaged flow fields associated with the second quadrant ͑Q2͒ event in the fully turbulent channel flow direct numerical simulation ͑DNS͒ database at Re = 395. The nonlinear evolution of the initial vortical structure is tracked by performing a spectral simulation. Background noise is introduced by adding small amplitude perturbations to the initial field or by imposing momentum forcing. The background noise gives rise to chaotic development of a hairpin packet. The hairpins become asymmetric, leading to much more complicated packet structures than are observed in the symmetric hairpin vortex train of the flow with a clean background. However, the chaotic packets show the same properties as the clean packet in terms of the rate of growth of vertical and spanwise dimensions and the distance between successive vortices, suggesting that the autogeneration mechanism is robust. The background noise leads to a decrease in the minimum value of the Q2 strength required to trigger autogeneration, indicating that background noise enhances autogeneration, especially in the buffer layer. The autogeneration process is more enhanced by the background noise with wavenumbers k x Ͻ k z . Conditionally averaged flow fields around the tall attached vortices in the hairpin packet show that they are associated with elongated low-momentum structures in the streamwise direction. Finally, the autogeneration process was tested in a real turbulent environment taken from an instantaneous field of a turbulent channel flow DNS. The generation of secondary hairpin vortices is clearly observed upstream of the primary hairpin.

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