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

doi:10.1007/S10652-012-9243-6

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

Journal Article•DOI•

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

Zhaowei Liu¹, Yongcan Chen¹, Dejun Zhu¹, Erqing Hui², Chunbo Jiang¹ - Show less +1 more•Institutions (2)

Tsinghua University¹, China Three Gorges Corporation²

17 May 2012-Environmental Fluid Mechanics (Springer Netherlands)-Vol. 12, Iss: 4, pp 341-346

TL;DR: In this article, an analytical solution for the vertical profiles of the horizontal velocity of channel flow with submerged shrub-like vegetation is investigated, and the velocity distribution of the whole column is determined in tandem with the logarithmic velocity profile above the vegetation.

read less

Abstract: 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.

...read moreread less

Citations

PDF

Open Access

More filters

Journal Article•DOI•

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

[...]

Wenxin Huai¹, Wei-Jie Wang¹, Yang Hu¹, Yuhong Zeng¹, Zhonghua Yang¹ - Show less +1 more•Institutions (1)

Wuhan University¹

01 Jul 2014-Advances in Water Resources

TL;DR: In this article, an analytical model for predicting the vertical distribution of mean streamwise velocity in an open channel with double-layered rigid vegetation is proposed, and good agreement between the analytical predictions and experimental data demonstrated the validity of the model.

...read moreread less

78 citations

Cites background from "Analytical model for vertical veloc..."

...[18] proposed an analytical solution for the vertical profile of horizontal velocity within submerged shrub-like vegetation based on the momentum theorem and mixing-length turbulence model....
[...]
...Close to the channel bed, there is a thin shear layer, which can be ignored in the analytical models [12,13,17,18]....
[...]

Journal Article•DOI•

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

[...]

Wenxin Huai¹, Wei-Jie Wang¹, Yuhong Zeng¹•Institutions (1)

Wuhan University¹

18 Dec 2013-Journal of Hydraulic Research

TL;DR: In this paper, 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.

...read moreread less

Abstract: 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

...read moreread less

37 citations

Cites methods from "Analytical model for vertical veloc..."

...For example, Li and Shen (1973) adopted 1.13 for rigid cylinders, Klaassen and Van Der Zwaard (1974) adopted 1.5 for fairly rigid shrubs, Saowapon and Kouwen (1989) adopted CD from 0 to 2.0 for flexible plastic cylinders, and Liu et al. (2012) adopted 1.5 for shrub-like vegetation....
[...]

Journal Article•DOI•

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

[...]

Xu-Feng Yan¹, Wing-hong Onyx Wai¹, Chi-Wai Li¹•Institutions (1)

Hong Kong Polytechnic University¹

28 Apr 2016-Environmental Fluid Mechanics

TL;DR: In this article, 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.

...read moreread less

Abstract: 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.

...read moreread less

34 citations

Cites methods from "Analytical model for vertical veloc..."

...Similar to submerged vegetation flow with negligible lateral boundary influence [9, 16], the analytical solution for the Environ Fluid Mech (2016) 16:807–832 809...
[...]

Journal Article•DOI•

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

[...]

Jaan H. Pu¹, Awesar Hussain¹, Yakun Guo¹, Nikolaos Vardakastanis¹, Prashanth Reddy Hanmaiahgari², Dennis Lam¹ - Show less +2 more•Institutions (2)

University of Bradford¹, Indian Institute of Technology Kharagpur²

01 Jun 2019-Water science and engineering

TL;DR: In this article, an analytical model that represents the streamwise velocity distribution for open channel flow with submerged flexible vegetation is studied, and a sensitivity analysis has been conducted to assess the influences of the drag (C D ) and friction (C f ) coefficients on the flow velocity.

...read moreread less

Abstract: 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.

...read moreread less

28 citations

Journal Article•DOI•

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

[...]

Wei-Jie Wang, Wenxin Huai¹, Shuolin Li², Ping Wang³, Yu-Fei Wang⁴, Jiao Zhang¹ - Show less +2 more•Institutions (4)

Wuhan University¹, Cornell University², Beijing Forestry University³, Polytechnic University of Catalonia⁴

01 Nov 2019-Journal of Hydrology

TL;DR: In this article, a new shape function is proposed for vegetation with variable frontal width in the vertical direction, where the frontal width exhibits a gradual increase in vertical direction from bottom up in the vegetation.

...read moreread less

24 citations

1
2
3
4
…
5
6

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

Momentum absorption by vegetation

[...]

A. S. Thom¹•Institutions (1)

University of Edinburgh¹

01 Oct 1971-Quarterly Journal of the Royal Meteorological Society

TL;DR: In this paper, measurements were made in a wind-tunnel of the drag on elements of a simply-structured artificial crop, and of the wind profiles above and within the crop.

...read moreread less

Abstract: Measurements were made in a wind-tunnel of the drag on elements of a simply-structured artificial crop, and of the wind profiles above and within the crop. Analysis demonstrates (i)that the drag force on an element of such an array can be calculated from the profile of the turbulent shear flow within the array, using the known (and unmodified), wind-tunnel value of the drag coefficient of the individual element; (ii)that the zero-plane displacement (d) of an aerodynamically rough surface can be identified with the level of action of the drag on its elements; and (iii)that von Karman's constant = 0.41 ± 0.03. The relation z0 = 0.36 (h – d) is suggested for the roughness parameter of vegetation of height h. Calculated values of the drag force, f, on unit column of a real stand of beans in the field, using individual-element drag coefficients (Cd) and measured wind speeds, give f = 3.5 τ0 where τ0 is the downward momentum flux derived from the shape of the wind profile above. On the evidence of conclusion (i) and the dense and complex nature of the bean canopy, the factor 3.5 is attributed to mutual sheltering of neighbouring canopy elements rather than as evidence that the Cd – values are modified by turbulent shear flow. For the artificial crop, and for the real crop, recognition of the wind-speed dependence of the individual-element drag coefficients gives values of eddy viscosity, KM, almost constant in the height range h/3 < z ⩽ h and significantly larger than those found when constant drag coefficients are assumed. Constant KM within a crop canopy is consistent with the wind profile u(z)/u(h) = {1 + α(1 – z/h)}−2: an explicit expression is given for the parameter α.

...read moreread less

573 citations

"Analytical model for vertical veloc..." refers methods in this paper

...With regards to the zero-plane displacement d , Thom [8] and Jackson [5] proposed a definition by integrating the shear stress from bed to vegetation top....
[...]
...If the flow above the vegetation follows the logarithmic function, the velocity profile over the water column is expressed as, u = ⎧⎨ ⎩ √ C1 [ (z/L + a)2 + b]n − u2s0 H(z) z ≤ k u∗ κ ln ( z−d z0 ) z > k (7) where κ is Von Karman’s constant, d is the zero-plane displacement which is located at a distance from the bed inside the vegetation, u∗ is the virtual bed stress velocity for the upper layer given by u∗ = √g(h − k)i and z0 is the length scale for bed roughness of the upper layer which is determined by the boundary condition that the flow velocity at the top of the vegetation equals the flow velocity of the overlying logarithmic profile z0 = (k − d) exp [ −κ √ C1 [ (k/L + a)2 + b]n − u2s0 H(k) /√ g(h − k)i ] (8) With regards to the zero-plane displacement d , Thom [8] and Jackson [5] proposed a definition by integrating the shear stress from bed to vegetation top....
[...]

Journal Article•DOI•

On the displacement height in the logarithmic velocity profile

[...]

P. S. Jackson¹•Institutions (1)

University of Auckland¹

01 Oct 1981-Journal of Fluid Mechanics

TL;DR: In this paper, the displacement height of rough-wall boundary layers is defined as the level at which the mean drag on the surface appears to act, which coincides with the average displacement thickness for the shear stress.

...read moreread less

Abstract: The displacement height appears in the logarithmic velocity profile for rough-wall boundary layers as a reference height for the vertical co-ordinate. It is shown that this height should be regarded as the level at which the mean drag on the surface appears to act. The equations of motion then show that this also coincides with the average displacement thickness for the shear stress.A simple analytical model, experimental results and dimensional analysis are all used to indicate how the displacement height depends upon the detailed geometry of the roughness elements.

...read moreread less

530 citations

Additional excerpts

...With regards to the zero-plane displacement d , Thom [8] and Jackson [5] proposed a definition by integrating the shear stress from bed to vegetation top....
[...]
...If the flow above the vegetation follows the logarithmic function, the velocity profile over the water column is expressed as, u = ⎧⎨ ⎩ √ C1 [ (z/L + a)2 + b]n − u2s0 H(z) z ≤ k u∗ κ ln ( z−d z0 ) z > k (7) where κ is Von Karman’s constant, d is the zero-plane displacement which is located at a distance from the bed inside the vegetation, u∗ is the virtual bed stress velocity for the upper layer given by u∗ = √g(h − k)i and z0 is the length scale for bed roughness of the upper layer which is determined by the boundary condition that the flow velocity at the top of the vegetation equals the flow velocity of the overlying logarithmic profile z0 = (k − d) exp [ −κ √ C1 [ (k/L + a)2 + b]n − u2s0 H(k) /√ g(h − k)i ] (8) With regards to the zero-plane displacement d , Thom [8] and Jackson [5] proposed a definition by integrating the shear stress from bed to vegetation top....
[...]

Journal Article•DOI•

On inducing equations for vegetation resistance

[...]

Martin J. Baptist¹, Vladan Babovic², J. Rodríguez Uthurburu³, Maarten Keijzer, R.E. Uittenbogaard, Arthur E. Mynett³, A. Verwey³ - Show less +3 more•Institutions (3)

Delft University of Technology¹, National University of Singapore², UNESCO-IHE Institute for Water Education³

01 Jul 2007-Journal of Hydraulic Research

TL;DR: In this paper, the authors describe the process of induction of equations for the description of vegetation-induced roughness from several angles, and present a numerical 1-DV k-e turbulence model which includes several important features related to the influence plants exhibit on the flow.

...read moreread less

Abstract: The paper describes the process of induction of equations for the description of vegetation-induced roughness from several angles. Firstly, it describes two approaches for obtaining theoretically well-founded analytical expressions for vegetation resistance. The first of the two is based on simplified assumptions for the vertical flow profile through and over vegetation, whereas the second is based on an analytical solution to the momentum balance for flow through and over vegetation. In addition to analytical expressions the paper also outlines a numerical 1-DV k–e turbulence model which includes several important features related to the influence plants exhibit on the flow. Last but not least, the paper presents a novel way of applying genetic programming to the results of the 1-DV model, in order to obtain an expression for roughness based on synthetic data. The resulting expressions are evaluated and compared with an independent data set of flume experiments

...read moreread less

373 citations

"Analytical model for vertical veloc..." refers background in this paper

...[1] developed a differential equation to represent the vertical profile of horizontal velocity within the submerged vegetation: 1 2 cpl d2u2 dz2 − 1 2 CDm Du 2 = −gi (1)...
[...]
...To provide more details about the vertical velocity distribution of the submerged vegetation flow, flow structures are investigated both in laboratory flume and in natural river and several analytical models are developed [6,7,1,3]....
[...]

Journal Article•DOI•

Effect of Riparian Vegetation on Flow Resistance and Flood Potential

[...]

Stephen E. Darby

01 May 1999-Journal of Hydraulic Engineering

TL;DR: In this article, an existing hydraulic model is modified to predict stage-discharge curves for channels with nonuniform cross sections, sand and gravel-bed materials, and flexible or non-flexible riparian vegetation.

...read moreread less

Abstract: An existing hydraulic model is modified to predict stage-discharge curves for channels with nonuniform cross sections, sand and gravel-bed materials, and flexible or nonflexible riparian vegetation. The model is based on a version of the flow momentum and continuity equations that account for lateral shear. The model accounts for the effects of vegetation using empirically calibrated flow resistance equations that incorporate measurable physical properties of vegetation. Separate flow resistance equations are used for flexible and nonflexible vegetation types. Simulated stage-discharge curves are compared with data obtained from three natural river channels. Discrepancies between simulated and observed data range between 2 and 45%, but most (∼70%) discrepancies were <15%. Sensitivity tests are performed to determine the effects of different types of riparian vegetation on friction factor and flood elevation. Surfaces covered by nonflexible vegetation are rougher than those covered with flexible riparian vegetation. Based on simulations at the three study sites, operational maintenance regimes are proposed that minimize flood risk, while maximizing the environmental benefits of a well-developed riparian vegetation cover.

...read moreread less

215 citations

"Analytical model for vertical veloc..." refers background in this paper

...The presence of vegetation within river systems will change their velocity profiles which are usually logarithmic for the channels with either rough or smooth beds [2]....
[...]

Journal Article•DOI•

Flow resistance in open channel flows with sparsely distributed bushes

[...]

Maurizio Righetti¹, Aronne Armanini¹•Institutions (1)

University of Trento¹

01 Dec 2002-Journal of Hydrology

TL;DR: In this article, the vertical distribution of mean velocity and turbulence stress have been measured with laser Doppler anemometry techniques, by means of spatial and time-averaging rules.

...read moreread less

149 citations

"Analytical model for vertical veloc..." refers background in this paper

...To provide more details about the vertical velocity distribution of the submerged vegetation flow, flow structures are investigated both in laboratory flume and in natural river and several analytical models are developed [6,7,1,3]....
[...]