This paper employs an input-output based approach to analyze convective velocities and the transport of fluctuations in turbulent channel flows. The convective velocity for a fluctuating quantity associated with streamwise-spanwise wavelength pairs at each wall-normal location is obtained through the maximization of the power spectral density associated with the linearized Navier-Stokes equations with a turbulent mean profile and delta-correlated Gaussian forcing. We first demonstrate that the mean convective velocities computed in this manner agree well with those reported previously in the literature. We then exploit the analytical framework to probe the underlying mechanisms contributing to the local convective velocity at different wall-normal locations by isolating the contributions of each spanwise-streamwise wavelength pair (flow scale). The resulting analysis suggests that the behavior of the convective velocity in the near-wall region is influenced by large scale structures further away from the wall. These structures resemble Townsend's attached eddies in the cross-plane, yet show incomplete similarity in the streamwise direction. We then investigate the role of each linear term in the momentum equation to isolate the contribution of the pressure, mean shear, and viscous effects to the deviation of the convective velocity from the mean at each flow scale. Our analysis highlights the role of the viscous effects, particularly in regards to large channel spanning structures whose influence extends to the near-wall region. The results of this work suggest the promise of an input-output approach for analyzing convective velocity across a range of flow scales using only the mean velocity profile.

中文翻译：

---

基于输入输出的湍流通道对流速度分析

本文采用基于输入输出的方法来分析对流速度和湍流通道流动中波动的传输。在每个壁法向位置与流向-展向波长对相关的波动量的对流速度是通过最大化与线性化纳维-斯托克斯方程相关的功率谱密度获得的，该方程具有湍流平均剖面和 delta 相关的高斯强迫。我们首先证明以这种方式计算的平均对流速度与先前在文献中报道的那些非常吻合。然后，我们利用分析框架通过隔离每个展向-流向波长对（流尺度）的贡献来探索在不同壁法线位置对局部对流速度做出贡献的潜在机制。结果分析表明，近壁区域的对流速度行为受离壁较远的大型结构的影响。这些结构在横向上类似于 Townsend 的附加涡流，但在流向方向上显示出不完全的相似性。然后，我们研究动量方程中每个线性项的作用，以隔离压力、平均剪切和粘性效应对每个流量尺度下对流速度与平均值偏差的贡献。我们的分析强调了粘性效应的作用，特别是对于影响延伸到近壁区域的大型通道跨越结构。