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The effect of wall deformations on wall turbulence is a topic of fundamental importance for the advancement of flow control strategies aimed at reducing the frictional drag. Dynamic wall deformations in the form of wall-normal of in-plane oscillations represents an area that is yet to be fully explored, and that can open a new realm of drag control strategies, as well as provide fresh insights into the structure of wall turbulence. In this study, we present several results from direct numerical simulations aimed at understanding the response of wall turbulence to standing wave-like wall motion, arranged in a checkerboard pattern. More specifically, here we target a low Reynolds number turbulent channel flow, featuring standing wave-like dynamic wall deformations on both bottom and top walls, with parameterizations in terms of the frequency of oscillations, roughness height, and spacing. We quantify the effect that this type of wall motion can have on the skin friction drag, various turbulent statistics, and turbulent flow structures. In addition, taking advantage of the periodicity and the symmetry of the flow, an improved phase-averaging procedure is introduced, which enhances the smoothness of the data. The results show that this type of dynamic wall deflection can have a significant effect on the turbulent flow in proximity to the wall, and that the variation of the spatial wavenumbers of the wall deflections can make a big difference. A slight total drag reduction, in the order of 2%, was observed for some combinations of wavenumbers and frequencies, especially for the highest streamwise wavenumber case.
Brockhaus et al. (Mon,) studied this question.