# Roughness, Inertia, and Diffusion Effects on Anomalous Transport in Rough Channels

## TL;DR

This paper investigates how roughness, inertia, and diffusion influence anomalous tracer transport in rough channels through simulations and stochastic modeling, revealing universal scaling laws and the importance of Lagrangian velocity statistics.

## Contribution

It introduces a comprehensive study combining simulations and stochastic models to understand the combined effects of roughness, inertia, and diffusion on transport in rough channels, including universal scaling laws.

## Key findings

- Pe controls first-passage time distributions
- Roughness effects become prominent at higher Re
- Universal power-law scaling at infinite Pe

## Abstract

We study how the complex interplay between roughness, inertia, and diffusion controls the tracer transport in rough channels. We first simulate the flow and tracer transport over wide ranges of channel roughness, Reynolds number ($Re$), and P\'eclet 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 with the increase in $Re$. The interplay between the roughness and $Re$ causes eddy 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 correlation. We finally predict the anomalous transport using a stochastic model that considers the Lagrangian velocity statistics.