A mixing‐length‐scale‐based analytical model for predicting velocity profiles of open‐channel flows with submerged rigid vegetation

Abstract

In open-channel flows with submerged vegetation, the vertical velocity profile can often be described by two layers: the vegetation layer in the lower region and the surface layer in the upper non-vegetated region. In this paper, a new mixing-length scale of eddy is proposed for predicting the vertical velocity profile of flow in an open-channel with submerged rigid vegetation. The analytical model of velocity profile is based on the momentum equation of flow where the turbulent eddy viscosity is assumed to have a linear relationship with the local velocity. The proposed model was tested against different datasets from the literature. The 22 datasets used cover a range of submergence [flow depth (H)/vegetation height (h) = 1.25 ~ 3.38], different vegetation densities of ah = 0.11 ~ 1.85 (a defined as the frontal area of the vegetation per unit volume) and bed slopes (S o = 1.8 × 10 −6 ~4.0 × 10 −3 ). This study showed that the proposed model can predict the velocity profiles well against all datasets, and that the mixing length scale of eddies (λ) is well related with both vegetation height (h) and flow depth of surface layer (i.e. the height of non-vegetation layer, H-h). Close examination of λ in the proposed model showed that when λ = 0.03 √ h(H − h), the model predicts vertical velocity profiles well for all datasets used except for very shallow submergence (i.e. H/h < 1.5).

An Improved Analytical Model for Vertical Velocity Distribution of Vegetated Channel Flows

“…In the evaluation of the above models and other models, Tang & Ali (2013) and Tang (2019a) showed that the predicted velocity distribution by the above mentioned models is acceptable only for certain experimental datasets, but they do not agree with other datasets. In addition, the predictions by these models show significant differences even for the same dataset.…”

“…The complexity of vegetated channel flow can be interpreted in multiple mechanisms over the depth of flow (Katul et al, 2011;Nikora et al, 2013;Huai et al, 2014). The multiple mechanisms over different layers of flow can be modelled independently (Carollo et al, 2002;Huai et al, 2014;Tang, 2018aTang, , 2018bSingh et al, 2019). As a pre-requisite for the analysis in resistance and pollutant mixing process of flow and so on, the vertical velocity distribution in vegetated channel flow has drawn great attention of researchers (e.g.…”

“…Tsujimoto & Kitamur, 1990, Shimizu & Tsujimoto, 1994Nepf & Koch, 1999;Ghisalberti & Nepf, 2004;Kubrak, et al, 2008;Tang & Knight, 2009;Tang et al, 2010Tang et al, , 2011Nguyen, 2012;Hao et al, 2014). Many investigators have attempted to predict vertical velocity distribution based on semi-empiricism and/or analytical solution of the momentum equation with closure schemes, in which the modelling of eddy viscosity is to describe the turbulent stresses (Klopstra et al, 1997;Meijer & Van Velzen, 1999;Defina & Bixio, 2005;Baptist et al, 2007;Huai, et al, 2009Huai, et al, , 2014Yang & Choi, 2010;Dimitris & Panayotis, 2011;Nepf, 2012;Nikora et al, 2013;Tang, 2018aTang, , 2019aSingh et al, 2019).…”

“…The flow structure in this region is governed through the mixing length of eddy and vertical turbulent transport of momentum from the surface flow, with the negligible contribution from the pressure gradient. The effect of the shear length scale can be related to the vegetation height and flow depth (Klopstra et al, 1997;Defina & Bixio, 2005;Tang, 2018aTang, , 2018bTang, , 2019aSingh et al, 2019).…”

“…These models are so-called two-layer or three-layer methods. In the layer of submerged vegetation, the analytical model of velocity distribution is based on the concept of mixing-layer analogy of eddy (Klopstra et al, 1997;Meijer & Van Velzen, 1999;Ghisalberti & Nepf, 2004;Defina & Bixio, 2005;Baptist et al, 2007;Huai, et al, 2009Huai, et al, , 2014Yang & Choi, 2010;Nepf, 2012;Tang, 2018a).…”