An extended version of the resolvent formulation is used to evaluate the use of anisotropic porous materials as passive flow control devices for turbulent channel flow. The effect of these porous substrates is introduced into the governing equations via a generalized version of Darcy's law. Model predictions show that materials with high streamwise permeability and low wall-normal permeability ($\phi_{xy} = k_{xx}/k_{yy}\gg1$) can suppress resolvent modes resembling the energetic near-wall cycle. Based on these predictions, two anisotropic porous substrates with $\phi_{xy} > 1$ and $\phi_{xy} 1$ relative to a smooth wall flow at identical bulk Reynolds number. A significant increase in friction is observed over the substrate with $\phi_{xy} < 1$. This increase in friction is linked to the emergence of spanwise rollers resembling Kelvin-Helmholtz vortices. Coherent structures extracted via POD analysis show qualitative agreement with model predictions.

中文翻译：

---

用于被动湍流控制的多孔材料的基于溶剂的设计和实验测试

溶剂配方的扩展版本用于评估各向异性多孔材料作为湍流通道流动的被动流动控制装置的使用。这些多孔基材的影响通过达西定律的广义版本引入到控制方程中。模型预测表明，具有高流向渗透率和低壁面法向渗透率（$\phi_{xy} = k_{xx}/k_{yy}\gg1$）的材料可以抑制类似于高能近壁循环的分解模式。基于这些预测，相对于相同体积雷诺数下的平滑壁流，具有 $\phi_{xy} > 1$ 和 $\phi_{xy} 1$ 的两个各向异性多孔基材。在 $\phi_{xy} < 1$ 的情况下，观察到在衬底上的摩擦显着增加。这种摩擦力的增加与类似于开尔文-亥姆霍兹涡旋的展向滚子的出现有关。通过 POD 分析提取的相干结构显示与模型预测的定性一致。