Coupling effect of wall slip and spanwise oscillation on drag reduction in turbulent channel flow

The coupling effect of the isotropic wall slip and the spanwise oscillation boundary conditions on the drag reduction and turbulence properties are studied by direct numerical simulations. As the slip length increases, the drag reduction gradually changes from the oscillation dominated to the slip dominated. The increase of slip length will decrease the maximum spanwise velocity of the fluid on the wall, which is responsible for the decreased ability of the oscillatory wall motion to reduce the skin-friction drag. The drag reduction decomposition shows that the contribution from the modifications of turbulent dynamics will undergo a shift from drag increase to drag reduction as the isotropic slip length increases. Compared with the respective no-slip reference flow, the drag reduction of wall slip in laminar and turbulent channel flows can be expressed in a unified form versus the outer scale slip length. Furthermore, many aspects of the turbulence properties are influenced by the coupling effect. First, the wall slip condenses the envelope range of the phase fluctuations caused by the oscillatory wall motion, as well as the magnitude of the periodic fluctuation of the phase-averaged friction coefficient. Second, an unexpected property of the coupled boundary condition is found that the existence of the Stoke layer delays the relaminarization process caused by the large slip length. Third, the wall slip would narrow the periodic inclination of the streaks and then inhibit the energy transfer process in the horizontal direction. Fourth, in terms of phase, the Stokes strain and the shear angle have the same lag phase with the spanwise velocity, while the hysteresis of turbulent dynamics leads to the larger lag phase of the streaks and phase-averaged friction coefficient. These new features are valuable for increasing knowledge on this topic.