We consider linear feedback flow control of the largest scales in an incompressible turbulent channel flow at a friction Reynolds number of $Re_\tau = 2000$. A linear model is formed by augmenting the Navier-Stokes equations with an eddy viscosity and linearizing it about the turbulent mean. Velocity perturbations are then generated by stochastically forcing the linear operator. The objective is to reduce the kinetic energy of these velocity perturbations at the largest scales using body forces. It is shown that a control set-up with a well-placed sensor and actuator performs comparably to either measuring the flow everywhere (while actuating it at a single wall height) or actuating the flow everywhere (while measuring it at a single wall height). This idealized configuration, therefore, can provide insight into how specific scales of turbulence are most effectively measured and actuated at low computational cost.

中文翻译：

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Reτ=2000 时壁面湍流中相干结构的线性控制

我们考虑在摩擦雷诺数为 $Re_\tau = 2000 $ 时不可压缩湍流通道流中最大尺度的线性反馈流控制。线性模型是通过用涡粘性增加 Navier-Stokes 方程并将其关于湍流平均值线性化来形成的。然后通过随机强制线性算子生成速度扰动。目标是使用体力在最大尺度上减少这些速度扰动的动能。结果表明，具有良好放置的传感器和执行器的控制装置的性能与测量各处流量（同时在单个壁高处驱动它）或在各处驱动流（同时在单个壁高处测量）的性能相当. 因此，这种理想化的配置