Linking turbulent eddies to suspended sediments in open channel flows

Modeling suspended sediment concentration in the turbulent open channel flow continues to draw significant research attention given its relevance to multidisciplinary problems across geophysics and hydrology. In terms of contemporary and emerging challenges, suspended sediments have been shown to interact with nano/microplastics via aggregation and settling processes in rivers and other water systems. Early studies linking turbulent diffusivity to suspended sediments were conducted based on an effective mixing length theory developed for turbulence. However, the energetics of eddies, a significant characteristic of turbulence, were not explicitly represented in these sediment models. To bridge this gap, a new perspective will be offered for representing suspended sediment concentration in such applications by providing a formulation that accommodates all scales of turbulent eddies. The approach is to implement a co-spectral budget (CSB) model that can relate the turbulent sediment flux to the local shear stress and the sediment properties. The CSB considers the pressure-redistribution term as a revised linear Rotta scheme in spectral form, resolving the isotropozation of mechanical production and particle-turbulence interaction with a scale-dependent de-correlation relaxation time. Provided a commonly accepted vertical velocity spectrum and standard constants from turbulence models, the CSB result can resolve all the effects from turbulent eddies of multiple length scales, Reynolds number, and Schmidt number.