Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation
Citations
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....
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...Close to the channel bed, there is a thin shear layer, which can be ignored in the analytical models [12,13,17,18]....
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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....
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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...
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28 citations
24 citations
References
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....
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...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....
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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....
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...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....
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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)...
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...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]....
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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]....
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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]....
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