We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, p. A2) showed that the resolvent-based estimator is optimal when the true space–time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models – an eddy-viscosity model and white-noise forcing – and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

中文翻译：

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使用壁测量的基于解析的湍流通道流估计

我们采用基于溶剂的方法来估计湍流通道内的速度和压力波动，其中摩擦雷诺数约为 180、550 和 1000，使用来自直接数值模拟 (DNS) 数据库的壁处剪切应力和压力的测量值。马提尼等。(J.流体机械。, 卷。900, 2021, p. A2) 表明，当使用真正的时空强迫统计时，基于解析器的估计器是最佳的，因此为任何线性估计器的准确性提供了上限。我们使用这个框架来确定可以从壁测量中线性估计的流动结构，并且我们描述了这些结构以及物理和波数空间中的估计误差。我们还将这些结果与使用近似强迫模型（涡粘性模型和白噪声强迫）获得的结果进行比较，并证明使用真实强迫统计的显着优势。所有模型都会导致精确到缓冲层的结果，但只有使用真正的强制统计才能准确估计大规模对数层结构，在整个渠道的估计和 DNS 结果之间存在显着相关性。涡粘性模型显示出一种中间行为，这可能与其部分捕获强迫颜色的能力有关。我们的结果表明，可以使用基于线性解析器的方法准确估计在通道壁上留下足迹的结构，并且大规模贴壁结构的存在可以通过对数层进行准确估计。