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 \(\lambda _z^+ > 400\). 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.

使用不仅在流向而且在展向具有周期性的流向行波（称为波机行波）控制完全发展的湍流通道流的直接数值模拟，以研究流向行波对减阻效果的展向变化。本研究中获得的最大减阻率小于展向均匀行波的情况。减阻率随着展向波长的增加而增加，在\(\lambda_z^+ > 400\)的范围内可以获得减阻效果. 根据相位平均雷诺剪切应力（RSS）分析，与展向相比，波机行波使流场在流向更均匀，在展向不均匀。 - 均匀行波。RSS 的湍流分量在波腹平面内的湍流分量在壁面附近被抑制，而在节点平面中的湍流分量在远离壁面的地方被显着抑制。使用 Fukagata-Iwamoto-Kasagi 恒等式的分析表明，在展向均匀行波的情况下，主要由于 RSS 的湍流分量的贡献显着降低而导致的减阻效果在一定程度上被在类似波机的行波的情况下，来自 RSS 的周期性（即色散）分量的贡献。