The behaviour of turbulent flow over anisotropic permeable substrates is studied using linear stability analysis and direct numerical simulations (DNS). The flow within the permeable substrate is modelled using the Brinkman equation, which is solved analytically to obtain the boundary conditions at the substrate-channel interface for both the DNS and the stability analysis. The DNS results show that the drag-reducing effect of the permeable substrate, caused by preferential streamwise slip, can be offset by the wall-normal permeability of the substrate. The latter is associated with the presence of large spanwise structures, typically associated to a Kelvin-Helmholtz-like instability. Linear stability analysis is used as a predictive tool to capture the onset of these drag-increasing Kelvin-Helmholtz rollers. It is shown that the appearance of these rollers is essentially driven by the wall-normal permeability Ky+$K_{y}^{+}$. When realistic permeable substrates are considered, the transpiration at the substrate-channel interface is wavelength-dependent. For substrates with low Ky+$K_{y}^{+}$, the wavelength-dependent transpiration inhibits the formation of large spanwise structures at the characteristic scales of the Kelvin-Helmholtz-like instability, thereby reducing the negative impact of wall-normal permeability.

中文翻译：

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使用各向异性可渗透基材降低湍流阻力

使用线性稳定性分析和直接数值模拟 (DNS) 研究湍流在各向异性可渗透基底上的行为。渗透性基质内的流动使用 Brinkman 方程建模，该方程被解析求解以获得用于 DNS 和稳定性分析的基质-通道界面处的边界条件。DNS 结果表明，由优先流向滑动引起的可渗透基底的减阻作用可以被基底的壁面法向渗透率抵消。后者与大展向结构的存在有关，通常与类似开尔文-亥姆霍兹的不稳定性有关。线性稳定性分析被用作一种预测工具来捕捉这些增加阻力的开尔文-亥姆霍兹滚子的开始。结果表明，这些滚子的出现基本上是由壁面法向渗透率 Ky+$K_{y}^{+}$ 驱动的。当考虑现实的可渗透基质时，基质-通道界面处的蒸腾作用与波长有关。对于具有低 Ky+$K_{y}^{+}$ 的底物，波长相关的蒸腾作用抑制了开尔文-亥姆霍兹样不稳定性特征尺度上大展向结构的形成，从而减少了壁面法向的负面影响渗透性。