Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, opposition control is only realizable if there is a degree of coherence between the sensor--actuator pairs of the control system (these sensors and actuators should typically be wall-based to avoid parasitic drag). As such, we here inspect the feasibility of real-time control of the near-wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from numerical simulations at $Re_\tau \approx 590$ and $ 2000$ are employed. It is shown that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region. Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers. Coherence values of 0.55 and 0.4, which are considerably lower than the maximum possible coherence 1, were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. This suggests that a closed-loop drag reduction scheme targeting near wall cycle of streaks alone will be of limited success in practice as the Reynolds number grows.

中文翻译：

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壁面流动中的近壁相干性及其对流动控制的影响

使用数值方法对壁界湍流中近壁条纹的能量循环进行对抗控制，已显示出减少阻力的希望。对于实际实施，只有在控制系统的传感器 - 执行器对之间存在一定程度的一致性时才能实现对立控制（这些传感器和执行器通常应基于墙壁以避免寄生阻力）。因此，我们在这里通过考虑可测量的壁面数量（壁面剪切应力波动）与流向和壁面法向速度波动之间的一致性来检查近壁面循环的实时控制的可行性。湍流边界层。使用来自 $Re_\tau\approx 590$ 和 $2000$ 数值模拟的同步空间和时间速度数据。结果表明，与壁面信号随机不相干的流向速度波动的谱能量与近壁面区域的雷诺数无关。因此，由于能量大尺度范围的增加，随机壁相干的流向能量分数随着雷诺数的增加而增长。因此，这意味着基于壁的控制系统能够以较高的雷诺数操纵离壁位置的总湍流能量的较大部分。在能谱中近壁峰处的流向和壁法向速度波动与流向波动摩擦速度之间分别发现了 0.55 和 0.4 的相干值，它们远低于最大可能的相干性 1。