A series of direct numerical simulation (DNSs) of the turbulent plane Couette flow were performed with various box lengths, L _x = 24h, 32h, 45h and 64h, where h is the channel height. The Reynolds numbers Re _w (= U _w h/ν) of 3000 and 8600 were chosen, where U _w is the relative wall speed between top and bottom walls and ν is the kinematic viscosity. In the core region, the meandering of the large-scale structure (LSS) has been captured with a long box size (L _x ≥ 32h). Correspondingly, the streamwise two-point correlation decreases and becomes negative at half the box length. The effect of the computational box size on the statistics, e.g. turbulence intensities, is also examined. Significant Reynolds-number dependence is observed in the streamwise LSS. For the higher Reynolds number, both the visualized instantaneous flow field and the pre-multiplied energy spectra show that the LSS can be present, with a finite wavelength of 21–32h in the streamwise direction and a spanwise spacing of 2.1–2.5h. The structure in the wall-normal direction is also discussed using the two-dimensional two-point correlations.

Flow states in plane Couette flow in a spanwise rotating frame of reference have been mapped experimentally in the parameter space spanned by the Reynolds number and rotation rate. Depending on the direction of rotation, the flow is either stabilized or destabilized. The experiments were made through flow visualization in a Couette flow apparatus mounted on a rotating table, where reflected flakes are mixed with the water to visualize the flow. Both short- and long-time exposures have been used: the short-time exposure gives an instantaneous picture of the turbulent flow field, whereas the long-time exposure averages the small, rapidly varying scales and gives a clearer representation of the large scales. A correlation technique involving the light intensity of the photographs made it possible to obtain, in an objective manner, both the spanwise and streamwise wavelengths of the flow structures. During these experiments 17 different flow regimes have been identified, both laminar and turbulent with and without roll cells, as well as states that can be described as transitional, i.e. states that contain both laminar and turbulent regions at the same time. Many of these flow states seem to be similar to those observed in Taylor–Couette flow.

Interscale energy transfer in wall turbulence has been intensively studied in recent years, and both forward (i.e. from larger to smaller scales) and reversed transfers of turbulent energy have been found, although their corresponding physical phenomena have not been revealed. In the present study, we perform direct numerical simulations of turbulent plane Couette flow with reduced-size computational domains, where either the streamwise or the spanwise domain size is reduced to its minimal length, aiming to elucidate the role of scale interactions in each direction. Our computational results with the streamwise-minimal domain suggest that the interplays between streamwise-elongated streaks and vortices smaller than the streamwise minimal length are the essential scale interactions for both the inner and the outer structures. We further show that these streamwise-independent and smaller-scale structures exchange energy through forward and reversed interscale energy transfers, and the reversed energy transfer maintains the energy production at larger scales. Based on the resemblance between the observed Reynolds-stress transport and the scenario of the self-sustaining cycle, we conjecture that the forward and reversed energy transfers mainly represent the streak instabilities and regeneration of streamwise vortices, respectively. Furthermore, the computation with the spanwise-minimal domain indicates that the interscale energy transfers observed by one-dimensional spanwise spectral analysis are likely related to the individual dynamics of each inner and outer structure, rather than representing their interactions.

The effect of viscoelastic contribution on wall-bounded turbulent flow of drag-reducing surfactant solution is investigated through direct numerical simulations (DNS). A series of DNS on turbulent channel flow is performed for different rheological properties at two different Reynolds numbers. It is found that high drag reduction is achieved by suppressing the turbulent contribution for the high Weissenberg number, and/or by decreasing the viscosity ratio and the effective viscosity. A highly drag-reduced turbulent flow at a high Reynolds number is mainly caused by the viscoelastic effect in the elastic layer, whereas the outer layer flow hardly affects the drag reduction. Moreover, we focus on the viscoelastic contribution term in the budget of Reynolds stress and its relation to the local flow pattern. It is shown that in the near-wall region of the highly drag-reduced flow a positive work done by viscoelastic stress is closely associated with vortex stretching that produces turbulent kinetic energy from stored elastic energy, whereas a negative one causes vortex compression.