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Roughness, inertia, and diffusion effects on anomalous transport in rough channel flows

Seonkyoo Yoon1 and Peter K. Kang1,2,*

  • 1Department of Earth and Environmental Sciences, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, Minnesota 55455, USA

  • *Corresponding author: pkkang@umn.edu
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Phys. Rev. Fluids 6, 014502 – Published 29 January, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.014502

Abstract

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.

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Phys. Rev. Fluids 6, 014502– Published 29 January, 2021
  • Received 21 May 2019
  • Accepted 6 January 2021
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