# Velocity Profile and Turbulence Structure Measurement Corrections for Sediment Transport-Induced Water-Worked Bed

## Abstract

**:**

## 1. Introduction

## 2. Experimental Descriptions

#### 2.1. Experimental Instrumentations

#### 2.2. ADV Device

_{2}in Equation (5) is introduced as an additional vertical velocity component with the three main velocities. Averaging W

_{1}and W

_{2}can reduce noise signal for the vertical velocity. As proven, the four-receiver ADV had presented velocity measurement with a higher SNR ratio than the three-receiver ADV due to the use of an extra receiver [17].

#### 2.3. Experimental Conditions

^{3}was feasible at each sampling point for the utilised ADV; however, this volume would be increased, if the measured point showed a low SNR ratio. All point measurements were recorded at a frequency of 100 Hz for a sampling duration of 5 min.

#### 2.4. Bed Settings

_{16}= 3.81 mm, d

_{50}= 6.62 mm and d

_{84}= 7.94 mm and a density of 2823.8 kg m

^{–3}. The natural river gravels were chosen, as it can achieve the water-worked bed condition more rapidly (as compared to sand or silt), where the stationary sediment bed was aimed to be created after long erosion and deposition. d

_{50}was used to estimate the representative Nikuradse’s equivalent roughness k

_{s}as suggested by Dey and Raikar [8].

^{–1}using a conveyor system. During the whole sedimentation process of amour layers settling, the flow in the water flume was retained at a uniform depth of 100 mm with 40.5 l s

^{–1}of discharge. It took nearly 5 full days of a continuous flash stream for the fully static water-worked rough bed to form, and the nonmovable bed condition was recorded if the average bed level changed throughout the whole channel was less than 0.2d

_{50}. After the settling phase was completed, the water depth was increased to 130 mm by the end gate, while the discharge was retained.

_{b}is the bedload transport, s is the relative density between solid and water, g is the gravitational acceleration, d is the sediment size, ${\tau}_{cr}$ is the dimensionless critical shear stress, $\tau $ is dimensionless shear stress ($={\tau}_{b}/\rho \left(s-1\right)gd$), ${\tau}_{b}$ is the bed shear stress, $\rho $ is the water density.

## 3. Bed Realignment Technique

## 4. Results and Discussion

#### 4.1. Velocity Distribution

_{o}is the flow reference vertical location from the rough bed crest where z

_{o}= 0.25 k

_{s}was found to estimate the reference level well. For the rough bed flow, κ = 0.44, B

_{r}= 7.4 and П = 0.0792 were used, while κ = 0.44, B

_{r}= 6.3 and П = 0.0767 were set for the water-worked bed flow [18]. The shear velocity was estimated as ${u}_{*}=\sqrt{gR{S}_{o}}$, where g is the gravitational acceleration, R is the hydraulic radius, and S

_{o}is the bed slope.

^{2}= 0.88, whereas the corrected data show a regression coefficient of r

^{2}= 0.93 when benchmarked by the law of wake. This comparison evidenced that the suggested realignment technique improves the averaged velocity from the measurements; however, the improvement has been proven to be not too significant. In Figure 5, the same comparison has been performed for the corrected and uncorrected data for the water-worked bed after long sediment flushing and settling. The uncorrected data give a regression coefficient of r

^{2}= 0.71 compared to the law of wake; but this regression has been enhanced to r

^{2}= 0.94 for the corrected data. With this finding, we can conclude that the proposed realignment method works reasonably well on the rough bed flow, but it improves the velocity point-measurement data of the water-worked bed more clearly.

_{s}value and more unpredictable law of wake’s constants and therefore present a more difficulty scenario for accurate near-bed velocity profile measurements especially at z/h ≤ 0.2 (as suggested by Cooper and Tait [14]; Pu et al. [18]). Referred to Figure 5, the near-bed velocity correction has been well performed to achieve high agreement with the calculated law of wake, and this demonstrates that the proposed method works for the flow within the sediment transport-induced water-worked bed. Practically, the presented method can also be used in field measurements to improve the real-world flow data.

#### 4.2. Turbulent Intensity Comparison

^{2}= 0.79 while the corrected data give r

^{2}= 0.91 based on the comparison with the exponential law. On the other hand, Figure 7 shows the uncorrected and corrected data’s regression coefficients to be r

^{2}= 0.82 and r

^{2}= 0.90, respectively. From Figure 6 and Figure 7, the well-packed rough and water-worked bed flows showed a similar magnitude of improvement in regression coefficient when the proposed realignment method was applied. This proved that the turbulent intensity dictated by the unidirectional velocity fluctuation can be improved by the proposed method; but the improvement on sediment transport-induced bedform (i.e., water-worked bed) is similar to the experimentally prepared bed. Due to this, it will be also crucial to investigate the effectiveness of the proposed approach to correct the multidirectional velocity fluctuations. In the view of this reason, we will be further investigating the Reynolds stress comparison in the coming section.

#### 4.3. Reynolds Stress Comparison

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Bed Condition | Q (l s^{−1}) | U (m s^{−1}) | h (m) | Fr (-) | u (m s^{−1}) |
---|---|---|---|---|---|

Well-packed rough | 40.5 | 0.69 | 0.13 | 0.61 | 0.054 |

Water-worked | 40.5 | 0.69 | 0.13 | 0.61 | 0.060 |

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Pu, J.H.
Velocity Profile and Turbulence Structure Measurement Corrections for Sediment Transport-Induced Water-Worked Bed. *Fluids* **2021**, *6*, 86.
https://doi.org/10.3390/fluids6020086

**AMA Style**

Pu JH.
Velocity Profile and Turbulence Structure Measurement Corrections for Sediment Transport-Induced Water-Worked Bed. *Fluids*. 2021; 6(2):86.
https://doi.org/10.3390/fluids6020086

**Chicago/Turabian Style**

Pu, Jaan H.
2021. "Velocity Profile and Turbulence Structure Measurement Corrections for Sediment Transport-Induced Water-Worked Bed" *Fluids* 6, no. 2: 86.
https://doi.org/10.3390/fluids6020086