Drag Reduction Effect of Streamwise Traveling Wave-Like Wall Deformation with Spanwise Displacement Variation in Turbulent Channel Flow

Direct numerical simulation of a fully developed turbulent channel flow controlled using a streamwise traveling wave having a periodicity not only in the streamwise direction but also in the spanwise direction, referred to as wave-machine-like traveling wave, is performed to investigate the impact of the spanwise variation of the streamwise traveling wave on the drag reduction effect. The maximum drag reduction rate attained in the present study is smaller than that in the case of the spanwise-uniform traveling wave. The drag reduction rate increases as the spanwise wavelength increases, and the drag reduction effect can be obtained in the range of λz+>400\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _z^+ > 400$$\end{document}. According to the analysis of the phased-averaged Reynolds shear stress (RSS), the wave-machine-like traveling wave makes the flow field more uniform in the streamwise direction and non-uniform in the spanwise direction, as compared to the case of spanwise-uniform traveling wave. While the turbulent component of RSS in the antinode plane is suppressed near the wall, that in the node plane is significantly suppressed far from the wall. An analysis using the Fukagata–Iwamoto–Kasagi identity shows that the drag reduction effect, which was primary due to the significant decrease in the contribution from the turbulent component of the RSS in the case of spanwise-uniform traveling wave, is partly deteriorated by the contribution from the periodic (i.e., dispersive) component of RSS in the case of wave-machine-like traveling wave.