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

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## Abstract

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## 1. Introduction

## 2. Experimental Methods and Program

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**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 (%) | $0.051$ |

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**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