# Deciphering Morphological Changes in a Sinuous River System by Higher-Order Velocity Moments

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods and Program

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Rozovskiῐ, I.L. Flow of Water in Bends of Open Channels; Academy of Sciences of the Ukrainian SSR: Kiev, Ukraine, 1957. [Google Scholar]
- Anwar, H.O. Turbulent structure in a river bend. J. Hydraul. Eng.
**1986**, 112, 657–669. [Google Scholar] [CrossRef] - De Vriend, H.J.; Geldof, H.J. Main flow velocity in short river bends. J. Hydraul. Eng.
**1983**, 109, 991–1011. [Google Scholar] [CrossRef] - Blanckaert, K.; Graf, W.H. Mean flow and turbulence in open-channel bend. J. Hydraul. Eng.
**2001**, 127, 835–847. [Google Scholar] [CrossRef] - Booij, R. Modeling the flow in curved tidal channels and rivers. In Proceedings of the International Conference on Estuaries and Coasts, Hangzhou, China, 9–11 November 2003; pp. 786–794. [Google Scholar]
- Sukhodolov, A.; Kaschtschejewa, E. Turbulent flow in a meander bend of a lowland river: Field measurements and preliminary results. In Proceedings of the River Flow 2010, Braunschweig, Germany, 8–10 September 2010; Dittrich, A., Koll, K., Aberle, J., Geisenhainer, P., Eds.; River Flow 2010. Karlsruhe: Bundesanstalt für Wasserbau. S. 309-316. [Google Scholar]
- Engel, F.L.; Rhoads, B.L. Velocity profiles and the structure of turbulence at the outer bank of a compound meander bend. Geomorphology
**2017**, 295, 191–201. [Google Scholar] [CrossRef] - Graf, W.H.; Blanckaert, K. Flow around bends in rivers. In Proceedings of the 2nd International Conference New Trends in Water and Environmental Engineering for Safety and Life: Eco-Compatible Solutions for Aquatic Environments, Capri, Italy, 24–28 June 2002; pp. 1–9. [Google Scholar]
- Blanckaert, K. Topographic steering, flow recirculation, velocity redistribution, and bed topography in sharp meander bends. Water Resour. Res.
**2010**, 46. [Google Scholar] [CrossRef] - Blanckaert, K. Analysis of coherent flow structures in a bend based on instantaneous-velocity profiling. In Proceedings of the 3rd International Symposium on Ultrasonic Doppler Methods for Fluid Mechanics and Fluid Engineering, EPFL, Lausanne, Switzerland, 9–11 September 2002. [Google Scholar]
- Esfahani, F.S.; Keshavarzi, A. Effect of different meander curvatures on spatial variation of coherent turbulent flow structure inside ingoing multi-bend river meanders. Stoch. Environ. Res. Risk Assess.
**2011**, 25, 913–928. [Google Scholar] [CrossRef] - Xu, D.; Bai, Y. Experimental study on the bed topography evolution in alluvial meandering rivers with various sinuousnesses. J. Hydro-Environ. Res.
**2013**, 7, 92–102. [Google Scholar] [CrossRef] - Binns, A.D.; da Silva, A.M.F. Meandering bed development time: Formulation and related experimental testing. Adv. Water Resour.
**2015**, 81, 152–160. [Google Scholar] [CrossRef] - Huggett, R.J. Fundamentals of Geomorphology, 4th ed.; Routledge—Taylor & Francis Group: New York, NY, USA, 2017. [Google Scholar]
- Da Silva, A.M.; Ebrahimi, M. Meandering Morphodynamics: Insights from Laboratory and Numerical Experiments and Beyond; American Society of Civil Engineers: Reston, VA, USA, 2017. [Google Scholar] [CrossRef]
- Whiting, P.J.; Dietrich, W.E. Experimental studies of bed topography and flow patterns in large-amplitude meanders: 2. Mechanisms. Water Resour. Res.
**1993**, 29, 3615–3622. [Google Scholar] [CrossRef] - Whiting, P.J.; Dietrich, W.E. Experimental studies of bed topography and flow patterns in large-amplitude meanders: 1. Observations. Water Resour. Res.
**1993**, 29, 3605–3614. [Google Scholar] [CrossRef] - Termini, D. Experimental observations of flow and bed processes in large-amplitude meandering flume. J. Hydraul. Eng.
**2009**, 135, 575–587. [Google Scholar] [CrossRef] - Luchi, R.; Zolezzi, G.; Tubino, M. Modelling mid-channel bars in meandering channels. Earth Surf. Process. Landf.
**2010**, 35, 902–917. [Google Scholar] [CrossRef] - Zhang, C.; Xu, M.; Hassan, M.A.; Chartrand, S.M.; Wang, Z.; Ma, Z. Experiment on morphological and hydraulic adjustments of step-pool unit to flow increase. Earth Surf. Process. Landf.
**2019**, 45, 280–294. [Google Scholar] [CrossRef] - Abidin, R.Z.; Sulaiman, M.S.; Yusoff, N. Erosion risk assessment: A case study of the Langat River bank in Malaysia. Int. Soil Water Conserv. Res.
**2017**, 5, 26–35. [Google Scholar] [CrossRef] - Choi, C.E.; Cui, Y.; Au, K.Y.K.; Liu, H.; Wang, J.; Liu, D.; Wang, H. Case study: Effects of a partial-debris dam on riverbank erosion in the Parlung Tsangpo River, China. Water
**2018**, 10, 250. [Google Scholar] [CrossRef][Green Version] - Engel, F.L.; Rhoads, B.L. Interaction among mean flow, turbulence, bed morphology, bank failures and channel planform in an evolving compound meander loop. Geomorphology
**2012**, 163, 70–83. [Google Scholar] [CrossRef] - Heller, V. Scale effects in physical hydraulic engineering models. J. Hydraul. Res.
**2011**, 49, 293–306. [Google Scholar] [CrossRef] - Peakall, J.; Ashworth, P.J.; Best, J.L. Meander-bend evolution, alluvial architecture, and the role of cohesion in sinuous river channels: A flume study. J. Sediment. Res.
**2007**, 77, 197–212. [Google Scholar] [CrossRef] - Braudrick, C.A.; Dietrich, W.E.; Leverich, G.T.; Sklar, L.S. Experimental evidence for the conditions necessary to sustain meandering in coarse-bedded rivers. Proc. Natl. Acad. Sci. USA
**2009**, 106, 16936–16941. [Google Scholar] [CrossRef][Green Version] - Coz, J.L.; Michalkova, M.; Hauet, A.; Comaj, M.; Dramais, G.; Holubová, K.; Piégay, H.; Paquier, A. Morphodynamics of the exit of a cutoff meander: Experimental findings from field and laboratory studies. Earth Surf. Process. Landf. J. Br. Geomorphol. Res. Group
**2010**, 35, 249–261. [Google Scholar] [CrossRef][Green Version] - Meneveau, C.; Marusic, I. Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech.
**2013**, 719. [Google Scholar] [CrossRef][Green Version] - De Silva, C.M.; Marusic, I.; Woodcock, J.D.; Meneveau, C. Scaling of second-and higher-order structure functions in turbulent boundary layers. J. Fluid Mech.
**2015**, 769, 654–686. [Google Scholar] [CrossRef][Green Version] - Sharma, A.; Kumar, B. High-Order Velocity Moments of Turbulent Boundary Layers in Seepage Affected Alluvial Channel. J. Fluids Eng.
**2018**, 140, 81204. [Google Scholar] [CrossRef] - Leopold, L.B.; Langbein, W.B. River meanders. Sci. Am.
**1966**, 214, 60–73. [Google Scholar] [CrossRef] - Yalin, M.S. River Mechanics; Pergamon Press: Oxford, UK, 1992. [Google Scholar]
- Yalin, M.S.; Da Silva, A.M.F. Fluvial Processes; IAHR Monograph: Delft, The Netherlands, 2001. [Google Scholar]
- Schwarz, A.C.; Plesniak, M.W.; Murthy, S.N.B. Response of turbulent boundary layers to multiple strain rates. J. Fluid Mech.
**2002**, 458, 333–377. [Google Scholar] [CrossRef] - Goring, D.G.; Nikora, V.I. Despiking acoustic Doppler velocimeter data. J. Hydraul. Eng.
**2002**, 128, 117–126. [Google Scholar] [CrossRef][Green Version] - Dey, S.; Das, R.; Gaudio, R.; Bose, S.K. Turbulence in mobile-bed streams. Acta Geophys.
**2012**, 60, 1547–1588. [Google Scholar] [CrossRef] - Deshpande, V.; Kumar, B. Turbulent flow structures in alluvial channels with curved cross-sections under conditions of downward seepage. Earth Surf. Process. Landf.
**2016**, 41, 1073–1087. [Google Scholar] [CrossRef] - Shams, M.; Ahmadi, G.; Smith, D.H. Computational modeling of flow and sediment transport and deposition in meandering rivers. Adv. Water Resour.
**2002**, 25, 689–699. [Google Scholar] [CrossRef] - Golden Software, LLC. 809 14th Street, Golden, Colorado 80401. Available online: https://www.goldensoftware.com/ (accessed on 10 March 2020).
- Rahman, M.; Nagata, N.; Hosoda, T.; Muramoto, Y. Experimental study on morphological process of meandering channels with bank erosion. Proc. Hydraul. Eng.
**1996**, 40, 947–952. [Google Scholar] [CrossRef] - Da Silva, A.M.F.; El-Tahawy, T.; Tape, W.D. Variation of flow pattern with sinuosity in sine-generated meandering streams. J. Hydraul. Eng.
**2006**, 132, 1003–1014. [Google Scholar] [CrossRef] - Nezu, I. Turbulent Structure in Open-Channel Flows. English Translation of the Japanese Dissertation of Iehisa Nezu. 1977. Available online: https://repository.tudelft.nl/islandora/object/uuid%3Aa41f39c2-fce6-4647-bd7a-1d412c720ed7 (accessed on 10 March 2020).
- Marusic, I.; Kunkel, G.J. Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids
**2003**, 15, 2461–2464. [Google Scholar] [CrossRef] - Hultmark, M.; Vallikivi, M.; Bailey, S.C.C.; Smits, A.J. Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett.
**2012**, 108, 94501. [Google Scholar] [CrossRef] [PubMed][Green Version]

**Figure 1.**Schematic diagram of the experimental setup showing: (

**a**) Side view of the experimental flume; (

**b**) plan view of the experimental setup; (

**c**) section $\mathrm{r}-\mathrm{r},\text{}\mathrm{s}-\mathrm{s},$ and $\mathrm{t}-\mathrm{t}$ where velocities were measured at locations 1, 2, 3, 4, and 5; (

**d**) sections from $\u201c\mathrm{a}\u201d$ to $\u201c\mathrm{q}\u201d$ where ultrasonic ranging system (URS) readings were made to track morphological changes.

**Figure 2.**Power spectra $\left[{\mathrm{F}}_{\mathrm{uu}}\left(\mathrm{f}\right){\mathrm{cm}}^{2}/\mathrm{s}\right]$ of unfiltered and filtered velocity time-series at outer and inner bends. ${\mathrm{F}}_{\mathrm{uu}}\left(\mathrm{f}\right)$ is the velocity power spectra of the streamwise velocity $\mathrm{u}$, which is a function of frequency $\mathrm{f}$ (in Hz).

**Figure 3.**Streamwise velocity profile at the outer (location 1) and inner bends (location 2) of the sinuous channel.

**Figure 4.**Contour plots of streamwise velocity at the bend cross-sections (

**a**) $\mathrm{r}-\mathrm{r},\left(b\right)\text{}\mathrm{s}-\mathrm{s},$ and (

**c**) $\mathrm{t}-\mathrm{t}$ of the sinuous channel.

**Figure 5.**Morphological changes along the second bend of the sinuous channel after 2, 6, and 10 h. This bend was selected because it was unaffected by the entry and exit conditions.

**Figure 6.**Cross-sectional morphological changes across the bend apex (section i) after 2, 4, 6, 8, and 10 h.

**Figure 7.**Streamwise velocity variance in turbulent boundary layers for flow at inner and outer bends of the sinuous river channel.

**Figure 8.**Premultiplied probability density functions (PDF) of normalized velocity fluctuations ${\mathrm{u}}^{+2\mathrm{p}}\mathrm{P}\left({\mathrm{u}}^{+}\right)$ at $\mathrm{z}/\mathrm{h}=0.08$ with moments (

**a**) $2\mathrm{p}=2$ and (

**b**) $2\mathrm{p}=4$. (

**c**) Moments of order $2\mathrm{p}=4$ for streamwise velocity as a function of wall-normal distance. Moments of different orders of streamwise velocity fluctuation as a function of wall normal distance for flow subjected to (

**d**) outer bend and (

**e**) inner bend.

**Figure 9.**Flatness factor as a function of the wall distance for outer and inner bend of the sinuous channel.

$\overline{\mathbf{u}}$ $\left(\mathbf{m}/\mathbf{s}\right)$ | $\overline{\mathbf{v}}$ $\left(\mathbf{m}/\mathbf{s}\right)$ | $\overline{\mathbf{w}}$ $\left(\mathbf{m}/\mathbf{s}\right)$ | ${\left(\overline{{\mathbf{u}}^{\mathbf{\prime}}{\mathbf{u}}^{\mathbf{\prime}}}\right)}^{0.5}$ $\left(\mathbf{m}/\mathbf{s}\right)$ | ${\left(\overline{{\mathbf{v}}^{\mathbf{\prime}}{\mathbf{v}}^{\mathbf{\prime}}}\right)}^{0.5}$ $\left(\mathbf{m}/\mathbf{s}\right)$ | ${\left(\overline{{\mathbf{w}}^{\mathbf{\prime}}{\mathbf{w}}^{\mathbf{\prime}}}\right)}^{0.5}$ $\left(\mathbf{m}/\mathbf{s}\right)$ | |
---|---|---|---|---|---|---|

Standard Deviation | $5\times {10}^{-3}$ | $6.18\times {10}^{-5}$ | $4.23\times {10}^{-5}$ | $1.84\times {10}^{-5}$ | $3.65\times {10}^{-5}$ | $1.8\times {10}^{-5}$ |

Uncertainty (%) | $0.221$ | $0.175$ | $0.192$ | $0.0177$ | $0.029$ | $0.039$ |

Standard Deviation | $6.19\times {10}^{-3}$ |
---|---|

Uncertainty (%) | $0.051$ |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Taye, J.; Barman, J.; Kumar, B.; Oliveto, G. Deciphering Morphological Changes in a Sinuous River System by Higher-Order Velocity Moments. *Water* **2020**, *12*, 772.
https://doi.org/10.3390/w12030772

**AMA Style**

Taye J, Barman J, Kumar B, Oliveto G. Deciphering Morphological Changes in a Sinuous River System by Higher-Order Velocity Moments. *Water*. 2020; 12(3):772.
https://doi.org/10.3390/w12030772

**Chicago/Turabian Style**

Taye, Jyotismita, Jyotirmoy Barman, Bimlesh Kumar, and Giuseppe Oliveto. 2020. "Deciphering Morphological Changes in a Sinuous River System by Higher-Order Velocity Moments" *Water* 12, no. 3: 772.
https://doi.org/10.3390/w12030772