Analytical Solution of Suspended Sediment Concentration Profile: Relevance of Dispersive Flow Term in Vegetated Channels

Abstract

Simulation of suspended sediment concentration (SSC) has great significance in predicting the sediment transport rate, vegetation growth, and the river ecosystem in channels. The present study focuses on investigating the vertical SSC profile in the vegetated open channel flows. To this end, a model of the dispersive flux is proposed in which the dispersive coefficient is expressed as partitioned linear profile above or below the half height of vegetation. The double‐averaging method, that is, time‐spatial average, is applied to investigate the vertical SSC profile in the vegetated open channel flows. The analytical solution of SSC in both submerged and emergent vegetated open channel flows is obtained by solving the vertical double‐averaging sediment advection‐diffusion equation. The morphological coefficient, a key factor of dispersive coefficient, is obtained by fitting the existing experimental data. The analytically predicted SSC agrees well with the experimental measurements, indicating that the proposed model can be used to accurately predict the SSC in the vegetated open channel flows. Results show that the dispersive term can be ignored in the region without vegetation, while the dispersive term has significant effect on the vertical SSC profile within the region of vegetation. The present study demonstrates that the dispersive coefficient is closely related to vegetation density, vegetation structure, and stem Reynolds number but has little relation with flow depth. With a few exceptions, the absolute value of the dispersive coefficient decreases with the increase of vegetation density and increases with the increase of stem Reynolds number in the submerged vegetated open channels.

Flow dynamics and sediment transport in vegetated rivers: A review

“…For within the vegetated region, the SSC profile decreased as a result that is different from the common profile patterns of suspended sediment over bare channels. The study of Huai et al [129] emphasized that the dispersion effect of spatial heterogeneity reduced by the existence of vegetation played an important role in the suspended sediment transport. They generalized the dispersion coefficient formula in the region of vegetation while ignoring it in the non-vegetated region.…”

“…In fact, each basic element of a river morphodynamics system is affected by riparian vegetation [152] , including the flow field, turbulent structure, sediment transport and river bed evolution [70,127,129,[153][154] . Moreover, riparian vegetation has a significant influence on river bank strength, which may lead to river bank collapse or increased bank stabilization.…”

A Co‐Spectral Budget Model Links Turbulent Eddies to Suspended Sediment Concentration in Channel Flows

“…(2018); W. Huai et al. (2020) is used here and is given by Cheng (1997) $$${w}_{s}=\frac{\nu }{{d}_{s}}{\left[\sqrt{25+1.2{d}_{s}^{2}{\left(\frac{{\rho }_{s}-\rho }{\rho }\frac{g}{{\nu }^{2}}\right)}^{2/3}}-5\right]}^{3/2},$$$ where ρ s is the sediment grain density with ρ s / ρ > 1, and d s is the sediment grain diameter. This w s is smaller than the Stokes settling velocity ( w st ) $$${w}_{st}=\frac{1}{18}\frac{g}{\nu }\left(\frac{{\rho }_{s}-\rho }{\rho }\right){d}_{s}^{2},$$$ except when the sediment particle Reynolds number Re sp = w s d s / ν ≪ 1.…”

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

“…With regards to the terminal sediment velocity, a simplified expression for w s that recovers many prior formulae (Tan et al, 2018;Huai et al, 2020) is used here and is given by (Cheng, 1997)…”

“…This operational definition is now standard in textbooks and research articles alike (Dey, 2014;Green & Coco, 2014;Dey & Ali, 2020). Despite some 80 years of research, the dominant factors controlling suspended sediment concentration (SSC) in streams continue to draw interest due to its multiple connections to ecosystem benefits and water quality degradation issues (Muste et al, 2005;Long & Pavelsky, 2013;Nazeer et al, 2014;Dai et al, 2016;Huai et al, 2019Huai et al, , 2020Tseng & Tinoco, 2020). High SSC can intercept photosynthetically active radiation necessary for sustaining submerged aquatic plants in lakes and rivers.…”