A co-spectral budget model links turbulent eddies to suspended sediment concentration in channel flows

TL;DR

This paper introduces a co-spectral budget model that explicitly links turbulent eddy energetics to suspended sediment concentration in channel flows, advancing sediment transport modeling by incorporating turbulence spectra.

Contribution

The novel co-spectral budget model explicitly accounts for turbulence energetics and eddy interactions, improving upon classical theories that use simplified mixing length or eddy diffusivity.

Findings

The model can recover Prandtl's and Rouse's equations under specific conditions.

It incorporates spectral shapes of vertical velocity and turbulence constants.

The approach provides a more physically-based description of sediment suspension.

Abstract

The vertical distribution of suspended sediment concentration (SSC) remains a subject of active research given its relevance to a plethora of problems in hydraulics, hydrology, ecology, and water quality control. Much of the classical theories developed over the course of 90 years represent the effects of turbulence on suspended sediments (SS) using an effective mixing length or eddy diffusivity without explicitly accounting for the energetics of turbulent eddies across scales. To address this gap, the turbulent flux of sediments is derived using a co-spectral budget (CSB) model that can be imminently used in SS and other fine particle transport models. The CSB closes the pressure-redistribution effect using a spectral linear Rotta scheme modified to include isotropoziation of production and interactions between turbulent eddies and sediment grains through a modified scale-dependent de-correlation time. The result is a formulation similar in complexity to the widely used Rouse's equation but with all characteristic scales, Reynolds number, and Schmidt number effects derived from well-established spectral shapes of the vertical velocity and accepted constants from turbulence models. Finally, the proposed CSB model can recover Prandtl's and Rouse's equations under restricted conditions.