# Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Theory

#### 2.2. Experimental Setup

_{50}) was 10.4 mm. The smooth surface of the channel bed was carefully prepared to eliminate large-scale variation in the bed topography. The artificial vegetation patch with a height of about 2.5 cm was placed over the middle pool section, which was 1.5 m long (Figure 1).

## 3. Results and Discussions

#### 3.1. Shear Velocity Distribution and Logarithmic Law

^{2}values show in Table 2. According to Figure 3, along the CAF (acceleration flow) section, the velocity data collected for the outer layer of the flow at a depth of 1.0 > z/h > 0.2 (till water surface) are above the regression line, implying a dominant adverse pressure gradient (∂p/∂x > 0). However, a favorable pressure gradient (∂p/∂x < 0) is dominant in the CDF (deceleration flow) and middle pool sections of the pool, where the data points collected for the outer layer of flow (1.0 > z/h > 0.2) are below the regression line. Approaching the sidewall, the validity of the logarithmic law for the velocity data near the bed region has also been confirmed. For flow with a relatively low Reynolds number, the boundary layer tends to be a laminar boundary layer. As the Reynolds number increases, the boundary layer becomes unstable with small disturbances. Further growth of these disturbances results in the transition to a turbulent boundary layer. Most practical flows involve high Reynolds numbers and turbulent boundary layers. Because of the three-dimensional interchanges in momentum, a turbulent boundary layer is thicker and has a larger wall velocity gradient than that of a laminar layer with the same Reynolds number. The increased momentum near the wall allows a turbulent boundary layer to withstand a larger unfavorable pressure gradient than a laminar layer without separating, but results in higher wall shear stress and drag.

#### 3.2. Velocity Distribution along the Pool

_{max}) of each velocity profile. Also, the depth related to a velocity point measurement (z) became dimensionless depth by dividing it to the flow depth (h).

#### 3.3. Quadrant Analysis of Bursting Events

#### 3.4. Distribution of Shear Stress and Longitudinal Turbulence Intensities

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Tabarestani, E.S.; Afzalimehr, H.; Pham, Q.B. Flow structure investigation over a pool-rife sequence in a variable width river. Acta Geophys.
**2022**, 70. [Google Scholar] [CrossRef] - Keller, E. Areal sorting of bed-load material: The hypothesis of velocity reversal: Reply. Geol. Soc. Am. Bull.
**1972**, 83, 915–918. [Google Scholar] [CrossRef] - Clifford, N.; Richards, K. The reversal hypothesis and teh maintenance of riffle-pool sequences: A review and field appraisal. In Lowland Floodplain Rivers: Geomorphological Perspectives; Wiley: Hoboken, NJ, USA, 1992; pp. 43–70. [Google Scholar]
- Clifford, N. Morphology and stage-dependent flow structure in a gravel-bed river. In Coherent Flow Struct. Open Channels; Wiley: Chichester, UK, 1996; pp. 545–566. [Google Scholar]
- Thompson, D.M. The role of vortex shedding in the scour of pools. Adv. Water Resour.
**2006**, 29, 121–129. [Google Scholar] [CrossRef] - Booker, D.; Sear, D.; Payne, A. Modelling three-dimensional flow structures and patterns of boundary shear stress in a natural pool–riffle sequence. Earth Surf. Process. Landf. J. Br. Geomorphol. Res. Group
**2001**, 26, 553–576. [Google Scholar] [CrossRef] - Wilkinson, S.N.; Keller, R.J.; Rutherfurd, I.D. Phase-shifts in shear stress as an explanation for the maintenance of pool–riffle sequences. Earth Surf. Process. Landf.
**2004**, 29, 737–753. [Google Scholar] [CrossRef] - MacWilliams, M.L., Jr.; Wheaton, J.M.; Pasternack, G.B.; Street, R.L.; Kitanidis, P.K. Flow convergence routing hypothesis for pool-riffle maintenance in alluvial rivers. Water Resour. Res.
**2006**, 42. [Google Scholar] [CrossRef][Green Version] - Sawyer, A.M.; Pasternack, G.B.; Moir, H.J.; Fulton, A.A. Riffle-pool maintenance and flow convergence routing observed on a large gravel-bed river. Geomorphology
**2010**, 114, 143–160. [Google Scholar] [CrossRef] - Chao, L.; Shan, Y.-Q.; Yang, K.-J.; Liu, X.-N. The characteristics of secondary flows in compound channels with vegetated floodplains. J. Hydrodyn. Ser. B
**2013**, 25, 422–429. [Google Scholar] - MacVicar, B.J.; Rennie, C.D. Flow and turbulence redistribution in a straight artificial pool. Water Resour. Res.
**2012**, 48. [Google Scholar] [CrossRef] - Fazel Najafabadi, E.; Afzalimehr, H.; Sui, J. A comparison of two-dimensional and three-dimensional flow structures over artificial pool-riffle sequences. Can. J. Civ. Eng.
**2017**, 44, 1084–1098. [Google Scholar] [CrossRef][Green Version] - Song, T.; Chiew, Y. Turbulence measurement in nonuniform open-channel flow using acoustic Doppler velocimeter (ADV). J. Eng. Mech.
**2001**, 127, 219–232. [Google Scholar] [CrossRef] - Okamoto, T.-A.; Nezu, I. Spatial evolution of coherent motions in finite-length vegetation patch flow. Environ. Fluid Mech.
**2013**, 13, 417–434. [Google Scholar] [CrossRef] - Huai, W.-X.; Zhang, J.; Katul, G.G.; Cheng, Y.-G.; Tang, X.; Wang, W.-J. The structure of turbulent flow through submerged flexible vegetation. J. Hydrodyn.
**2019**, 31, 274–292. [Google Scholar] [CrossRef] - Huai, W.; Zeng, Y.; Xu, Z.; Yang, Z. Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation. Adv. Water Resour.
**2009**, 32, 487–492. [Google Scholar] [CrossRef] - Jahadi, M.; Afzalimehr, H.; Ashrafizaadeh, M.; Kumar, B. A numerical study on hydraulic resistance in flow with vegetation patch. ISH J. Hydraul. Eng.
**2022**, 28, 243–250. [Google Scholar] [CrossRef] - Nosrati, K.; Afzalimehr, H.; Sui, J. Interaction of Irregular Distribution of Submerged Rigid Vegetation and Flow within a Straight Pool. Water
**2022**, 14, 2036. [Google Scholar] [CrossRef] - Wang, J.; He, G.; Dey, S.; Fang, H. Influence of submerged flexible vegetation on turbulence in an open-channel flow. J. Fluid Mech.
**2022**, 947, A31. [Google Scholar] [CrossRef] - Shahmohammadi, R.; Afzalimehr, H.; Sui, J. Impacts of Turbulent Flow over a Channel Bed with a Vegetation Patch on the Incipient Motion of Sediment. Can. J. Civ. Eng.
**2018**, 45, 803–816. [Google Scholar] [CrossRef] - D’Ippolito, A.; Calomino, F.; Penna, N.; Dey, S.; Gaudio, R. Simulation of accelerated subcritical flow profiles in an open channel with emergent rigid vegetation. Appl. Sci.
**2022**, 12, 6960. [Google Scholar] [CrossRef] - Afzalimehr, H.; Riazi, P.; Jahadi, M.; Singh, V.P. Effect of vegetation patches on flow structures and the estimation of friction factor. ISH J. Hydraul. Eng.
**2021**, 27, 390–400. [Google Scholar] [CrossRef] - Stephan, U.; Gutknecht, D. Hydraulic resistance of submerged flexible vegetation. J. Hydrol.
**2002**, 269, 27–43. [Google Scholar] [CrossRef] - Nepf, H.; Ghisalberti, M. Flow and transport in channels with submerged vegetation. Acta Geophys.
**2008**, 56, 753–777. [Google Scholar] [CrossRef] - Luhar, M.; Rominger, J.; Nepf, H. Interaction between flow, transport and vegetation spatial structure. Environ. Fluid Mech.
**2008**, 8, 423–439. [Google Scholar] [CrossRef] - Nepf, H.M.; Vivoni, E. Flow structure in depth-limited, vegetated flow. J. Geophys. Res. Ocean.
**2000**, 105, 28547–28557. [Google Scholar] [CrossRef] - Afzalimehr, H.; Subhasish, D. Influence of bank vegetation and gravel bed on velocity and Reynolds stress distributions. Int. J. Sediment Res.
**2009**, 24, 236–246. [Google Scholar] [CrossRef] - Fazlollahi, A.; Afzalimehr, H.; Sui, J. Effect of slope angle of an artificial pool on distributions of turbulence. Int. J. Sediment Res.
**2015**, 30, 93–99. [Google Scholar] [CrossRef] - MacVicar, B.; Obach, L. Shear stress and hydrodynamic recovery over bedforms of different lengths in a straight channel. J. Hydraul. Eng.
**2015**, 141, 04015025. [Google Scholar] [CrossRef] - Nezu, I.; Rodi, W. Open-channel flow measurements with a laser Doppler anemometer. J. Hydraul. Eng.
**1986**, 112, 335–355. [Google Scholar] [CrossRef] - Afzalimehr, H.; Rennie, C.D. Determination of bed shear stress in gravel-bed rivers using boundary-layer parameters. Hydrol. Sci. J.
**2009**, 54, 147–159. [Google Scholar] [CrossRef][Green Version] - Afzalimehr, H.; Moghbel, R.; Gallichand, J.; Sui, J. Investigation of turbulence characteristics in channel with dense vegetation. Int. J. Sediment Res.
**2011**, 26, 269–282. [Google Scholar] [CrossRef] - MacVicar, B.; Roy, A. Sediment mobility in a forced riffle-pool. Geomorphology
**2011**, 125, 445–456. [Google Scholar] [CrossRef] - Carling, P.A.; Orr, H.G. Morphology of riffle–pool sequences in the River Severn, England. Earth Surf. Process. Landf. J. Br. Geomorphol. Res. Group
**2000**, 25, 369–384. [Google Scholar] [CrossRef] - Przyborowski, Ł.; Łoboda, A.M.; Bialik, R.J. Effect of two distinct patches of Myriophyllum species on downstream turbulence in a natural river. Acta Geophys.
**2019**, 67, 987–997. [Google Scholar] [CrossRef][Green Version] - Mayaud, J.R.; Wiggs, G.F.; Bailey, R.M. Dynamics of skimming flow in the wake of a vegetation patch. Aeolian Res.
**2016**, 22, 141–151. [Google Scholar] [CrossRef][Green Version] - Robinson, S.K. Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech.
**1991**, 23, 601–639. [Google Scholar] [CrossRef] - Poggi, D.; Katul, G.; Albertson, J. Momentum transfer and turbulent kinetic energy budgets within a dense model canopy. Bound.-Layer Meteorol.
**2004**, 111, 589–614. [Google Scholar] [CrossRef] - Dey, S.; Nath, T.K. Turbulence characteristics in flows subjected to boundary injection and suction. J. Eng. Mech.
**2010**, 136, 877–888. [Google Scholar] [CrossRef] - Parvizi, P.; Afzalimehr, H.; Singh, V.P. Impact of pool and vegetated bottom on turbulant flow structure. Int. J. Hydraul. Eng.
**2021**, 10, 8–18. [Google Scholar] - Afzalimehr, H.; Anctil, F. Accelerating shear velocity in gravel-bed channels. Hydrol. Sci. J.
**2000**, 45, 113–124. [Google Scholar] [CrossRef][Green Version] - Kironoto, B.; Graf, W.H.; Reynolds. Turbulence characteristics in rough non-uniform open-channel flow. Proc. Inst. Civ. Eng.-Water Marit. Energy
**1995**, 112, 336–348. [Google Scholar] [CrossRef] - Afzalimehr, H. Effect of non-uniformity of flow on velocity and turbulence intensities over a cobble-bed. Hydrol. Process. Int. J.
**2010**, 24, 331–341. [Google Scholar] [CrossRef] - Najafabadi, E.F.; Afzalimehr, H.; Rowiński, P.M. Flow structure through a fluvial pool-riffle sequence–Case study. J. Hydro-Environ. Res.
**2018**, 19, 1–15. [Google Scholar] [CrossRef] - Coles, D. The law of the wake in the turbulent boundary layer. J. Fluid Mech.
**1956**, 1, 191–226. [Google Scholar] [CrossRef][Green Version] - Thornton, C.I.; Abt, S.R.; Morris, C.E.; Fischenich, J.C. Calculating shear stress at channel-overbank interfaces in straight channels with vegetated floodplains. J. Hydraul. Eng.
**2000**, 126, 929–936. [Google Scholar] [CrossRef] - MacVicar, B.J.; Rennie, C.D. Lateral distribution of turbulence and secondary currents in non-uniform open channel flow. In Proceedings of the 33rd IAHR Congress: Water Engineering for a Sustainable Environment Hydraulics, Vancouver, BC, Canada, 9–14 August 2009; pp. 1908–1915. [Google Scholar]

**Figure 2.**Distributions of shear velocity determined using two methods: (

**A**) Clauser’s method; (

**B**) the boundary layer method.

**Figure 4.**Distributions of stream-wise velocity profiles. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h= 2.7; blue line: second axis over vegetated bed with w/h = 2.

**Figure 5.**Distributions of velocity profiles. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h = 2.7; blue line: second axis over vegetated bed with w/h = 2.

**Figure 7.**Distribution of Reynolds shear stress. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h = 2.7; blue line: second axis over vegetated bed with w/h = 2.

**Figure 8.**Distribution of stream-wise RMS of turbulence intensity. Note: green line: central axis over vegetated bed with w/h = 2; black line: central axis over sandy bed with w/h = 2; gray line: central axis over vegetated bed with w/h = 2.7; blue line: second axis over vegetated bed with w/h = 2.

Q (L/s) | H (m) | W (m) | U_{avg} (cm/s) | W/H | Re × 10^{4} | Fr |
---|---|---|---|---|---|---|

10 | 0.20 | 0.4 | 12.5 | 2.0 | 2.5 | 0.09 |

10 | 0.15 | 0.4 | 16.7 | 2.7 | 2.5 | 0.13 |

x | Equation | ${\mathbf{R}}^{2}$ | ${\mathbf{U}}_{*}$ | f | |
---|---|---|---|---|---|

Central Axis | CDF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0116\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0321$ | 0.98 | 0.00464 | 0.011 |

Middle Sect. | $\text{}\mathrm{u}/{\mathrm{u}}_{*}=0.02\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0538$ | 0.90 | 0.008 | 0.032 | |

CAF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0274\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0644$ | 0.96 | 0.0108 | 0.059 | |

Second Axis | CDF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0106\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0204$ | 0.89 | 0.0042 | 0.009 |

Middle Sect. | $\mathrm{u}/{\mathrm{u}}_{*}=0.0151\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.0333$ | 0.97 | 0.006 | 0.018 | |

CAF Section | $\mathrm{u}/{\mathrm{u}}_{*}=0.0268\mathrm{ln}(\mathrm{z}/{\mathrm{k}}_{\mathrm{s}})+0.054$ | 0.93 | 0.0105 | 0.058 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Parvizi, P.; Afzalimehr, H.; Sui, J.; Raeisifar, H.R.; Eftekhari, A.R. Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study. *Water* **2023**, *15*, 205.
https://doi.org/10.3390/w15010205

**AMA Style**

Parvizi P, Afzalimehr H, Sui J, Raeisifar HR, Eftekhari AR. Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study. *Water*. 2023; 15(1):205.
https://doi.org/10.3390/w15010205

**Chicago/Turabian Style**

Parvizi, Parsa, Hossein Afzalimehr, Jueyi Sui, Hamid Reza Raeisifar, and Ali Reza Eftekhari. 2023. "Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study" *Water* 15, no. 1: 205.
https://doi.org/10.3390/w15010205