Three-Dimensional Hole Size (3DHS) Approach for Water Flow Turbulence Analysis over Emerging Sand Bars: Flume-Scale Experiments

Abstract

The many hydrodynamic implications associated with the geomorphological evolution of braided rivers are still not profoundly examined in both experimental and numerical analyses, due to the generation of three-dimensional turbulence structures around sediment bars. In this experimental research, the 3D velocity fields were measured through an acoustic Doppler velocimeter during flume-scale laboratory experimental runs over an emerging sand bar model, to reproduce the hydrodynamic conditions of real braided rivers, and the 3D Turbulent Kinetic Energy (TKE) components were analyzed and discussed here in detail. Given the three-dimensionality of the examined water flow in the proximity of the experimental bar, the statistical analysis of the octagonal bursting events was applied to analyze and discuss the different flume-scale 3D turbulence structures. The main novelty of this study is the proposal of the 3D Hole Size (3DHS) analysis, used for separating the extreme events observed in the experimental runs from the low-intensity events.

1. Introduction

Alluvial rivers characterized by high fluvial energy are typically affected by braiding phenomena, and the emergence of sediment bars is considered the prominent origin of complex morphologies associated with their formation [1,2]. The morphological variations occurring in braided streams are closely related to bank erosion, as a direct consequence of water flow—sediment transport interplay over time [3,4,5,6].

In this framework, the proper analysis of the main turbulence traits induced by the presence of bars within braided rivers is crucial from both morphological and hydrodynamic perspectives [7,8,9,10,11,12]. Among others, McSherry et al. [13] and Jalalabadi et al. [14] have observed that bursting turbulent events can be effectively coupled to the classical threshold shear stress theory for the prediction of particles entrainment mechanisms [15,16,17]. In recent hydro-geomorphological numerical and experimental research, the study of the coherent structures corresponding to emerging bars was analyzed for correlating sediment transport to instantaneous bursting events [18,19,20,21,22,23]. In hydrodynamics, the study of the 2D turbulent flow structures in the vicinity of the wall is generally performed by applying the well-known quadrant events analysis [24,25], whilst it is not sufficiently rigorous and satisfactory when analyzing 3D water flows [26,27,28,29]. In these cases, Leary and Schmeeckle [30] and Schobesberger et al. [31] have recently applied the so-called analysis of the octagonal bursting events [32,33,34], also known as octant events analysis, for overpassing the classical Reynolds stress approach [35,36].

The goal of the present experimental study is the analysis of the flume-scale 3D turbulence traits observable in the proximity of an emerging bar model. The 3D Turbulent Kinetic Energy (hereinafter indicated as TKE) components were evaluated here, and the whole flow turbulence was then examined by analyzing the octagonal bursting events approach. Following the study of Guan et al. [37] among others, the so-defined 3D Hole Size (3DHS) method was proposed in this study for segregating the extreme events from the low-intensity ones at the proximity of the examined emerging sand bar for the first time in the analysis of the turbulence traits observed during flume-scale laboratory experiments.

2. Materials and Methods

2.1. Laboratory Experiments

As shown in Figure 1, the experimental runs were carried out in a 3 m wide, 1 m deep, and 12 m long concrete flume located in the River Engineering Laboratory of the Department of Water Resources Development and Management at the Roorkee Indian Institute of Technology (India), under constant bed slope and discharge values of 0.005 and 0.25 m³ s⁻¹, respectively. The x direction corresponds to the water flow direction.

In the present experimental study, the 3D velocity components over x, y, and z directions in the proximity of the examined emerging sand bar [38,39,40,41,42,43], respectively indicated as streamwise (u), spanwise (v), and vertical (w) velocity components, were measured by using a 4-beam down-looking acoustic Doppler velocimeter (ADV) device [44,45,46,47,48] with an acquisition frequency of 20 Hz. The time-series data having a signal average Correlation coefficient—the average correlation between acoustic wave signals recorded by each couple of ADV beams—of less than 0.70 were excluded from the further data processing [49,50,51,52]. Due to the massive presence of sediment particles during the runs, all the experiments were carried out in clear water conditions. The shear stress in the flume is kept below the critical shear stress.

The results of the error analysis of ADV measurements are shown in

Table 1. Values of errors ADV measurements (in mm s⁻¹).

Flow Velocity Range (mm s−1)	ADV Error Range (mm s−1)
±50	±0.88
±100	±0.83
±200	±1.01

.

The results of the previous analysis indicate that the velocity errors in ADV measurement lie in the typical range of flume-scale experimental analysis, as highlighted by Nikou et al. [51].

Aiming at reducing as much as possible the well-known fluid dynamic end-wall effects on the turbulent water flow behaviour in the proximity of the examined emerging sand bar [50,51], the concrete flume’s width was increased in the central region, as shown in Figure 1.

The bed of the experimental concrete flume was composed of uniform grading sand, having a value of d₅₀ equal to 0.25 mm, with d₅₀ indicating the so-called mass-median-diameter of the sediments’ particle size distribution, as shown by many previous studies of ecohydraulic, environmental, and river engineering interest [53,54,55,56,57,58,59,60,61]. At each experimental run, the 3D velocity components were measured at 24 different points belonging to a measuring grid composed of 10 cm × 10 cm cells, and only 12 measuring points were selected for the further experimental analyses, named from “1” to “12”.

In more detail, the experimental emerging sand bar was kept at a constant depth of 32 cm for all runs, while the submergence ratio, defined as the ratio of the bar height to the water level, was different at each run. The bed elevation measurements were computed aiming at assuring that positive values indicate the depositional region while negative values indicate the scouring. In the present study case, the only experimental run 1R was performed with no emerging bar in the flume.

The experimental flume-scale conditions adopted in the present flume-scale study are indicated in

Table 2. Details of the experimental runs performed in this study: l (cm), b (cm). and h_b (cm) are the major and the minor dimension, and the height from the flume bed of the emerging sand bar model, respectively, while h_b/h is the submergence ratio.

Experimental Run	hb/h	b × l × hb
1R	-	-
2R	0.25	80 × 130 × 8
3R	0.31	80 × 130 × 10
4R	0.41	80 × 130 × 13
5R	0.47	80 × 130 × 15
6R	0.53	80 × 130 × 17
7R	0.59	80 × 130 × 19
8R	0.66	80 × 130 × 21
9R	0.72	80 × 130 × 23
10R	0.81	80 × 130 × 26
11R	0.88	80 × 130 × 28
12R	0.90	80 × 130 × 29

.

Since the hydrodynamic effect of turbulence bursting events is prevailing close to the experimental flume bed [62,63,64], the 3D velocity components were measured at the near-bed flume region, along 15 relative depths z/h, where z is the elevation of each measuring point on the emerging sand bar from the flume bed and h is the measured water level: 0.031, 0.038, 0.047, 0.056, 0.063, 0.069, 0.071, 0.073, 0.075, 0.078, 0.081, 0.083, 0.087, 0.093, and 0.097.

2.2. Experimental TKE Analysis

In the present experimental study case, the so-defined total TKE was computed by applying the following equation [65]:

$$\mathrm{TKE}=\frac{1}{2}\left(\overline{{{\mathrm{u}}^{\prime }}^2}+\overline{{{\mathrm{v}}^{\prime }}^2}+\overline{{{\mathrm{w}}^{\prime }}^2}\right),$$

(1)

where u′, v′, and w′ are the so-called 3D velocity fluctuation components over x, y, and z axes, respectively.

The three-dimensional TKE components in x, y, and z directions were then obtained as follows:

$${\mathrm{TKE}}_{\mathrm{x}}=\frac{1}{2}\overline{{{\mathrm{u}}^{\prime }}^2},$$

(2)

$${\mathrm{TKE}}_{\mathrm{y}}=\frac{1}{2}\overline{{{\mathrm{v}}^{\prime }}^2},$$

(3)

and

$${\mathrm{TKE}}_{\mathrm{z}}=\frac{1}{2}\overline{{{\mathrm{w}}^{\prime }}^2}.$$

(4)

In Equations (1)–(4) the horizontal top bars indicate Reynolds-type time-average values of the 3D velocity fluctuation components.

2.3. Analysis of Octagonal Bursting Events

In the present experimental study, the 3D flow structures induced by the experimental emerging sand bar were analyzed by applying the so-called octagonal bursting events approach [66], based on the sign of the experimental three-dimensional velocity fluctuations components [67,68,69].

The occurrence probabilities associated with each octagonal bursting event P_ζ = n_ζ/N in the single octant ζ, where n_ζ is the total amount of bursting events associated with each octant ζ, and N represents the total extension of the single examined ADV signal for all octants [70,71,72,73,74,75].

The detailed schematic overview of the eight classes of occurrence probabilities associated with the octagonal turbulence bursting events, namely from P₁ to P₈, is shown in the following Figure 2.

2.4. Analysis of Three-Dimensional Hole Size (3DHS)

As remarked by Di Bernardino [76] among others, low-intensity octagonal turbulence bursting events do not furnish any contribution to the turbulent burst, then it is possible applying the concept of Hole size analysis, used in fluid dynamics for the experimental analysis of 2D bursting events [77,78,79], in regions where the water flow is highly three-dimensional. In these cases, the combination of the Hole Size approach with octagonal turbulence bursting events analysis is extremely useful for distinguishing the extreme octagonal events from the low-intensity ones. Therefore, the three-dimensional Hole Size (3DHS) analysis is a novel threshold method proposed in the present experimental study for stretching the capabilities of the 2D Hole size analysis to the study of the 3D octagonal turbulence bursting events [80,81].

In analogy with the 2D Hole size [82,83,84,85,86,87], the 3DHS analysis was employed here for extracting from all the ADV time-series velocity signals the 3D turbulent velocity values higher than H times the product of the root mean square of the three velocity fluctuation components: |u′ v′ w′| > H

$\overline{{\mathrm{u}}^{\prime }{\mathrm{v}}^{\prime }\mathrm{w}}$.

3. Results and Discussion

3.1. Experimental TKE Analysis

The depth-averaged contour maps of TKE components over x, y, and z directions are shown in detail in Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7 for the experimental runs 1R, 2R, 4R, 6R, and 10R, respectively. In all Figures, L is the total length of the reference grid in the x direction, while the origin of the x and y axes is located at the bar bottom, at its center.

It emerges from the observation of Figure 3a–c that, for 1R run, no defined turbulence pattern can be recognized, and extremely low TKE values over x, y, and z directions were observed. This is due to the absence of the emerging sand bar. In more detail, TKE_x and TKE_y contour maps showed very poor fixed patterns, with decreasing values at growing transverse distances y/L. As indicated in Figure 4a–c, high-value TKE_x and TKE_y contours were retrieved near the upstream end of the examined emerging sand bar at the experimental run 2R, with a decreasing behavior towards its downstream end, while TKE_z contours do not furnish any fixed turbulence structure. Also, it was possible observing from the direct comparison of Figure 5, Figure 6 and Figure 7 that the values of the TKE components in the three directions increase with h_b/h, indicating that the augmentation in the height of the examined emerging sand bar induced high turbulence production trends.

3.2. Analysis of Octagonal Bursting Events

The following Figure 8, Figure 9, Figure 10 and Figure 11 illustrate the contour maps of depth-averaged occurrence probabilities associated with each octagonal bursting event, for the experimental runs 2R, 4R, 6R, and 10R, respectively.

From the comparative analysis of Figure 8, Figure 9, Figure 10 and Figure 11, it was detected that the even octagonal bursting events (P₂, P₄, P₆, and P₈) were dominant in the case of transverse distances y/L ≤ 0.2, while the odd octagonal bursting events (P₁, P₃, P₅, and P₇) play a crucial role for values of y/L > 0.2.

In addition, it was possible to observe that the peak occurrence probabilities associated with both even and odd octagonal bursting events appeared in the three-dimensional water flow region located between x/L ≤ 0.4 and 0.6 < x/L ≤ 1.0, and between y/L ≤ 0.2 and y/L > 0.2.

3.3. Analysis of Three-Dimensional Hole Size (3DHS)

Figure 12, Figure 13, Figure 14 and Figure 15 display, respectively, the variations in the occurrence probabilities of the octagonal bursting events (P₁–P₈) as a function of 3DHS at the measuring points “2”, “4”, “6”, and “10” for the experimental runs 2R, 4R, 6R, and 10R.

As reported in Figure 12, the depth-averaged occurrence probability corresponding to even octagonal bursting events is noticeably larger (at least two times) than that associated with odd ones at the measuring points “2” and “4”, placed near the upstream end of the emerging sand bar, while it decreases with 3DHS values systematically. On the contrary, nearby the downstream end of the experimental bar, at the measuring points “6” and “10”, the depth-averaged occurrence probabilities corresponding to the odd octagonal turbulence bursting events were higher than those observed in the case of even bursting events [88,89,90,91,92,93,94].

From the analysis of Figure 13, Figure 14 and Figure 15, it was possible to detect that the depth-averaged occurrence probabilities associated with even octagonal bursting turbulence events grew with increasing h_b/h values at the upstream end of the examined bar, and the same hydrodynamic pattern was recognized in the odd events close to the downstream end of the emerging sand bar [95,96,97,98,99].

The potential of the 3D water turbulence analysis reported in the present experimental study can be certainly increased through the support of the most advanced reinforcement and deep learning approaches, widely employed in recent ecohydraulic studies dealing with water resources management [100,101,102,103].

4. Conclusions

The present experimental research represents an extremely useful insight into the comprehension of the hydrodynamic interaction between local streambed elevation changes and 3D turbulent bursting events observed in the vicinity of the emerging sand bar.

An innovative threshold method based on the so-defined 3D Hole Size (3DHS) analysis was proposed here to study the 3D water flow structures observed over the examined emerging sand bar, obtained by extending the theoretical background of the well-known 2D Hole Size approach [104,105,106,107].

The experimental outcomes of the analysis performed in this work well indicate that the three-dimensional water flow fields induced by the presence of the emerging bar produced high values of even and odd octagonal bursting events near the upstream and the downstream end of the experimental bar model, respectively. Following the 3DHS methodology, it was observed that the occurrence probability of dominant events further increases with increasing 3DHS and h_b/h values. The main goal of furnishing a useful and simple tool for both hydrodynamic and environmental researchers for the analysis of 3D turbulence over braided rivers was accomplished through the present flume-scale experimental study.