Analytical model of the mean velocity distribution in an open channel with double-layered rigid vegetation

A two-layer model for predicting the vertical distribution of stream-wise velocity in open channel flow with submerged flexible vegetation is proposed Using the predicted deflection height of the flexible vegetation determined via the large-deflection cantilever beam theory, the flow is vertically separated into a bottom vegetation layer and an upper free water layer, and corresponding momentum equations for each layer are formulated In the bottom vegetation layer, the resistance caused by the deflected plants is calculated accounting for plant bending rather than adopting the existing resistance formula for erect rigid vegetation For the upper free water layer, a new type of polynomial velocity distribution is suggested instead of the traditional logarithmic velocity distribution to obtain a zero velocity gradient at the water surface To validate the proposed model, the published experimental data are employed

Two-layer model for open channel flow with submerged flexible vegetation

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (
 $$\partial \overline{u}/\partial z < 0$$
 ) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (
 $$- \overline{{u^{\prime}w^{\prime}}} < 0$$
 ) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

In this paper, an analytical model that represents the streamwise velocity distribution for open channel flow with submerged flexible vegetation is studied. In the present vegetated flow modelling, the whole flow field has been separated into two layers vertically: a vegetated layer and a non-vegetated free-water layer. Within the vegetated layer, an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted. In the non-vegetated layer, a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated. Based on the studied analytical model, a sensitivity analysis has been conducted to assess the influences of the drag ( C D ) and friction ( C f ) coefficients on the flow velocity. The investigated ranges of C D and C f have also been compared to published values. The findings suggest that the C D and C f values are non-constant at different depths and vegetation densities, unlike the constant values commonly suggested in literature. This phenomenon is particularly clear for flows with flexible vegetation, which is characterised by large deflection.

Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction

Analytical solutions of velocity profile in flow through submerged vegetation with variable frontal width

An analytical solution for the vertical profiles of the horizontal velocity of channel flow with submerged shrub-like vegetation is investigated in this paper. At first, a shape function is proposed to fit the diameter change of different types of shrub-like vegetation. Using the momentum theorem and the mixing-length turbulence model, an analytical solution for the vertical profile of the horizontal velocity within the vegetation is obtained. The velocity distribution of the whole column is determined in tandem with the logarithmic velocity profile above the vegetation. The solution is compared with experimental data in excellent agreement. The results show that the flow above the vegetation has a logarithmic velocity profile while the flow within the vegetation is impacted greatly by the shape and density of vegetation. The flows within shrub-like vegetations are non-uniform and vary inversely with the shrub diameter.

Chunbo Jiang

Papers

Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation