We study how the complex interplay between channel roughness, inertia, and diffusion controls tracer transport in rough channel flows. We first simulate flow and tracer transport over wide ranges of channel roughness, Reynolds number (Re), and Péclet number (Pe) observable in nature. Pe exerts a first-order control on first-passage time distributions, and the effect of roughness on the tracer transport becomes evident as Re increases. The interplay between the roughness and Re causes recirculating flows, which intensify or suppress anomalous transport depending on Pe. At infinite Pe, the late-time scaling follows a universal power-law scaling, which is explained by conducting a scaling analysis. With extensive numerical simulations and stochastic modeling, we show that the roughness, inertia, and diffusion effects are encoded in Lagrangian velocity statistics represented by velocity distribution and velocity correlation. We successfully reproduce anomalous transport using an upscaled stochastic model that honors the key Lagrangian velocity statistics.

中文翻译：

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粗糙，惯性和扩散对粗糙通道流动中异常输送的影响

我们研究了在粗糙的通道流中，通道粗糙度，惯性和扩散之间的复杂相互作用如何控制示踪剂的运输。我们首先模拟自然界中可观测到的大范围的通道粗糙度，雷诺数（Re）和佩克利数（Pe）上的流量和示踪剂传输。Pe对首次通过时间分布进行一阶控制，并且随着Re的增加，粗糙度对示踪剂传输的影响变得明显。粗糙度和Re之间的相互作用会导致循环流动，从而加剧或抑制取决于Pe的异常传输。在无穷大Pe处，后期缩放遵循通用幂律缩放，​​这通过进行缩放分析来解释。通过大量的数值模拟和随机建模，我们证明了粗糙度，惯性，扩散效应以速度分布和速度相关性表示在拉格朗日速度统计中。我们使用高级随机模型成功地重现了异常输运，该模型兑现了关键的拉格朗日速度统计信息。