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

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 (Formula presented.), the model predicts vertical velocity profiles well for all datasets used except for very shallow submergence (i.e. H/h < 1.5).