Spatially developing drag reduction across a finite oscillating wall

The spatial evolution of a turbulent boundary layer at í µí±…í µí±’ τ = 430 developing across a finite spanwise oscillating wall is investigated with normalised oscillation period of í µí±‡ + ≈ 101 and amplitude í µí°´+µí°´+ ≈ 7 corresponding to a skin friction reduction of 32%. The spatial distribution of skin friction is estimated adopting a recently introduced near wall data nonlinear regression method based on the arctangent function, which circumvents the requirement of high wall normal resolution to capture the linear sub-layer. The method viability is assessed with reference data, and the trends of measurement errors are well reproduced in the analysis of the current data. The local impact of the control action is examined by evaluating the spatial development of scalar fields of turbulence statistics as well as conditional quadrant analysis to link the onset and recovery transients to turbulence events. The boundary layer response is observed to follow an exponential decay law for the skin friction spatial evolution. The decay length-scale corresponds to 0.7 boundary layer thicknesses δ for the onset transient and 1δ for the recovery one. Second-order statistics display shorter transients, owed to the dependence on short-scales compared to the integral nature of skin friction.