The Impact of Footprints of Large-Scale Outer Structures on the Near-Wall Layer in the Presence of Drag-Reducing Spanwise Wall Motion

This study is motivated by the observation that the drag-reduction effectiveness achieved by the imposition of oscillatory spanwise wall motion declines with Reynolds number. The question thus posed is whether the decline is linked to the increasingly strong influence of large-scale outer structures in the log layer on the near-wall turbulence, in general, and the streak strength in the viscosity-affected layer, in particular - a process referred to as modulation. This question is addressed via an extensive statistical analysis of DNS data for a channel flow at a friction Reynolds number 1020, subjected to oscillatory spanwise wall motion at a nominal wall-scaled period of 100. The analysis rests on a separation of turbulent scales by means of the Empirical Mode Decomposition. This method is used to derive conditional statistics of small-scale motions and skin friction subject to prescribed intensity of large-scale motions - referred to as footprinting. It is shown that the large-scale fluctuations are responsible, directly on their own, for roughly 30% to the skin friction. Positive large-scale fluctuations are also shown to be the cause of a major amplification of small-scale streaks, relative to weak attenuation by negative fluctuations. This highly asymmetric process is likely to be indirectly influential on the drag-reduction process, although it is not possible to identify this indirect effect in quantitative terms as part of the present analysis.