The work on the type of spatial oscillation been performed using DNS of flow through the combination of spatial and temporal wall oscillation. Only marginal improvement on the drag reduction was obtained (Skote, 2011). The numerical code and grid are the same as in the previous simulation of an oscillating turbulent boundary layer by Yudhistira and Skote who also showed that the grid is sufficiently fine. In developing the code a pseudo-spectral method is employed (Skote, 2011). All quantities are nondimensionalized by the free stream velocity (U) and the displacement thickness at the starting point of the simulation where the flow is laminar. The Reynolds number based on the momentum thickness varies between 418 and 750 in the region for the unmanipulated boundary. Modifications have been made thus allowing for streamwise modulation of the spanwise wall velocity. Resolutions used for the simulation were 800 modes in the streamwise direction, 201 in wall-normal direction, and 144 modes in the spanwise direction. The sampling time for the reference case was 6000 in time units. In the simulation presented, the maximum wall velocity and wavelength are set to 0.857 and 58.17, respectively. The wall forcing is of the same magnitude as the freestream velocity and the flow, therefore, deviates substantially from the unmanipulated boundary layer. Additional simulation is required so that an investigation of a much weaker and more practical wall forcing is got (Skote, 2011).
The qualitative similarity between responses to temporal and spatial forces strengthens the theory advanced by Viotti. The theory is that temporal forcing could be translated to spatial forcing through the use of a convection velocity of near-wall turbulence fluctuations. This relates to the oscillations period and wavelength through (λx+ =Um+T+. For direction comparison between the present spatial case and temporal simulation, T+) would be set to 130 if the estimated value of U+w=10 is used.