Transport relaxation time and length scales in turbulent suspensions

TL;DR

This paper derives a first-order relaxation model for sediment flux in turbulent flows, identifying key length and time scales, and validates predictions with experimental data for erosion and deposition scenarios.

Contribution

It introduces a first-order relaxation equation for sediment flux and links relaxation scales to flow and sediment parameters, validated by experiments.

Findings

Relaxation length scale: HU/V_fall

Relaxation time scale: H/V_fall

Model predictions agree with flume experiments

Abstract

We show that in a turbulent flow transporting suspended sediment, the unsaturated sediment flux $q(x,t)$ can be described by a first-order relaxation equation. From a mode analysis of the advection-diffusion equation for the particle concentration, the relaxation length and time scales of the dominant mode are shown to be the deposition length $H U/V_{\rm fall}$ and deposition time $H/V_{\rm fall}$, where $H$ is the flow depth, $U$ the mean flow velocity and $V_{\rm fall}$ the sediment settling velocity. This result is expected to be particularly relevant for the case of sediment transport in slowly varying flows, where the flux is never far from saturation. Predictions are shown to be in quantitative agreement with flume experiments, for both net erosion and net deposition situations.