# Experimental investigation of light particles transport in a tidal bore generated in a flume

Lionel Thomas, W Reichl, Yann Devaux, Anthony Beaudoin, Laurent David

► To cite this version:

Lionel Thomas, W Reichl, Yann Devaux, Anthony Beaudoin, Laurent David. Experimental investigation of light particles transport in a tidal bore generated in a flume. Sébastien Erpicum; Benjamin Dewals; Pierre Archambeau; Michel Pirotton. Sustainable Hydraulics in the Era of Global Change. Advances in Water Engineering and Research, CRC Press, pp.478-484, 2016, 978-1138029774. hal-02970887

HAL Id: hal-02970887

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Submitted on 9 Dec 2025

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# Experimental investigation of light particles transport in a tidal bore generated in a flume

L. Thomas, W. Reichl, Y. Devaux, A. Beaudouin & L. David

Axe HydEE, Département D2, Institut Pprime

Université de Poitiers · CNRS · ISAE-ENSMA, Poitiers, France

**ABSTRACT:** Tidal bores are natural flows that can have a strong impact on river ecosystems. Recently, there has been a regain of interest in this flow, for example in China. Many in-situ measurement campaigns have been performed, but they are very limited concerning the spatial resolution. Studies in the lab inside flumes, although questionable concerning their similitude to real tidal bores, can give new insights to understand the impact of such phenomena on the river sediments. In this study, optical measurement techniques (stereo-PIV and PTV coupled) are used to add some understanding of the influence of moving bores on the sediment transport. Four Froude numbers are investigated. The trajectories and their stability are observed, and it is shown that for undular bores, the impact on the trajectories is weak, while strong effects are observed in the breaking bore case.

## 1 INTRODUCTION

Tidal bores are natural flows that can have a strong impact on rivers ecosystems. Although a great deal of work has been devoted to these interactions, this complex phenomenon still retains an unexplained part for which new insights and new tools may be of some interest. Many investigations have studied the hydrodynamic interactions between the river flow and the tidal bore and their impacts on the sediment transport (Chen (2003), Chanson (2005), Simon et al. (2011), Fan et al. (2012)). The passage of the tidal bore generates a mixing zone of fine sediments (Kjerfve and Ferreira (1993), Wolanski et al. (2004), Chanson (2005)). These studies highlight scouring the muddy bottom and suspending materials for the passage of the bore. The undular bores induce the most intense sediment transport, as the whelps help keep sediment suspended Chanson and Tan (2010). The authors highlight for each type of bore, the possible movements of the particles. For an undular bore, particles have a helical path with maximum vertical rise in the ridges and advection downstream in the hollows. For the breaking bore, in the upper part of the flow, the particles have a pseudo-chaotic movement and near the bottom, the particles have the same behavior as to an undular bore. Recently in laboratory, David et al. (014a) and David et al. (014b) have measured the instantaneous velocity fields during the arrival of bore and showed the different turbulent flows

inside the water column in regards to several flow generation conditions. To better understand the impact of such phenomena on the sediment transport, laboratory measurements are carried out with two simultaneous optical technics (stereo-PIV and PTV coupled). In the paper, the experiment will be first presented and will follow by description of the measurement technics. The hydrodynamic results will be after presented in an Eulerian and a Lagrangian point of view for four different flow cases. Finally the sediment transport will be characterized and compared to the hydrodynamic characteristics.

## 2 EXPERIMENT

### 2.1 *Experimental set-up*

For the experiment we used an open water channel with a length of 8 m and a width of 0.4 m which can be seen in figure 1. The used worm pump had a speed control so that the flow rate could be fixed. The homogeneous behaviour of the inlet flow was ensured by a honeycomb grid followed by a convergent. In order to create a wave similar to the tidal bore in nature, a shutter door had been installed downstream of the measurement. This door was automatically moving downwards into the flow. The resulting increase of water depth led to the creation of a wave traveling upstream. This closing door was also used as a trigger for the other measurements. The first of these
<figure><img src="image_2.png" /><figcaption>Figure 1: Sketch of the experimental setup</figcaption></figure>

<table><caption>Table 1: Particles used for the measurements and filter used to separate the fluorescent signals.</caption><thead><tr><th>Material</th><th>density</th><th>diameter</th><th>dye</th><th>filter</th></tr></thead><tbody><tr><td>Vestosint</td><td>1.06</td><td>20 µm</td><td>Rhodamine6G</td><td>550 µm</td></tr><tr><td>PMMA</td><td>1.2</td><td>50 µm</td><td>Nile Red</td><td>610 µm</td></tr><tr><td>PMMA</td><td>1.2</td><td>300 µm</td><td>Nile Red</td><td>610 µm</td></tr></tbody></table>

measurements gave the water level at different positions over time. For this purpose, acoustic sensors had been installed on top of the channel, two upstream of the PIV field and two downstream. These have been recording at a rate of 200Hz. To get the necessary data for PIV and PTV, a laser sheet was used which was located at the centre of the channel parallel to the side walls. The used Darwin Duo Laser created a double pulse at 500 Hz with 15 mJ energy per single pulse. For the TR-PIV (Time Resolved PIV), two cameras of the type Photron SA1 with ten bits have been used, located at both sides of the channel, with an angle of about 20°. These two have been set up according to the Scheimpflug condition. For the PTV measurement, a camera of type Photron 8 bits APX RS has been used which has been positioned perpendicular to the flow.

## 2.2 Particles

For the measurements, three types of particles have been used with two types of fluorescent colour applied to them. Moreover, two band filters have been found to match the wavelengths of these colours. All these are shown in table 2.2. The coating of these particles as well as the testing with different filters have been done in the lab by Patrick Braud. Physically speaking, the laser beams are hitting the coated particles which are diffusing the light over a certain range of wavelength. The band filters are connected to the lenses of the cameras so that they only record

<figure><img src="image_3.png" /><figcaption>Figure 2: Emission spectrum of the Rhodamine 6G, and signal received by the cameras through the different optical filters.</figcaption></figure>

part of the signal. Figure 2 shows the diffused light of the PMMA particles marked with Rhodamine B as well as the two used filters. Figure 3 shows the diffused light of the PMMA particles marked with Nile-Red and again the two filters. The 550nm filter will be used for particles marked with Rhodamine B and the 610nm filter will be used for particles marked with Nile-Red. In both figures it can be seen that the particles can also be seen on the wrong filter even though with a much lower intensity. This error needed to be corrected by some later filtering during the post-processing, using thresholding.

## 2.3 Flow configurations

A tidal bore is a positive surge travelling upstream, it is also called a hydraulic jump in translation. If one moves with the bore, ie the hydraulic jump is fixed in a translating reference frame, the surge can be steadily followed. The upstream velocity and the bore celerity are respectively $U_f$ and $U_b$ and the upstream water depth is $h$. The Froude number based on the initial water elevation is calculated in the moving frame as
<figure><img src="image_4.png" /><figcaption>Figure 3: Emission spectrum of the Rhodamine 6G, and signal received by the cameras through the different optical filters.</figcaption></figure>

<table><caption>Table 2: Particles used for the measurements and filter used to separate the fluorescent signals.</caption><thead><tr><th>h (m)</th><th>U<sub>f</sub> (m/s)</th><th>U<sub>b</sub> (m/s)</th><th>Fr</th><th>type</th></tr></thead><tbody><tr><td>0.118</td><td>0.353</td><td>0.859</td><td>1.13</td><td>undular</td></tr><tr><td>0.0940</td><td>0.665</td><td>0.595</td><td>1.31</td><td>mixed</td></tr><tr><td>0.0735</td><td>0.567</td><td>0.644</td><td>1.44</td><td>mixed</td></tr><tr><td>0.1435</td><td>0.871</td><td>1.01</td><td>1.58</td><td>breaking</td></tr></tbody></table>

follows:

$$Fr = \frac{U_f + U_b}{\sqrt{gh}} \qquad (1)$$

Four flow configurations corresponding two four different Froude numbers have been investigated. Three of them are similar to previous studies (David et al. (014a)) and the last is for a low Froude number with undular characteristics. They are summarized in table 2.

## 2.4 Image processing

### stereo-PIV

The images were first cleaned using a background subtraction, a Laplacian and a thresholding. The images were masked using the measurement of the water depth using acoustic sensors. The images were dewarped using the camera models, obtained via a calibration procedure. The camera models were adjusted in order to be sure that the lines of sight are crossing on the particles. This is a delicate step, but it is necessary in order to avoid biases. Moreover, it can also correct the position of the cameras when it has moved during an experiment. The images were correlated using the FTEE correlation algorithm (Jeon et al. (2014)), which is a PIV algorithm adapted to time resolved measurements, and giving velocity field with good trajectories approximations. The velocity fields (two components) obtained for each camera were combined (Caluaud and David (2004)) to get the final velocity field (three components).

### PTV

The images were processed in the same way as for the stereo-PIV. A PTV algorithm was used to follow the particles. The first step was initialized

<figure><img src="image_5.png" /><figcaption>Figure 4: Spatio-temporal diagram of the velocity field for Fr=1.13. The vectors represent the 2D velocity field. The colours represent the horizontal velocity component.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 5: Spatio-temporal diagram of the velocity field for Fr=1.31. The vectors represent the 2D velocity field. The colours represent the horizontal velocity component.</figcaption></figure>

using the velocity fields obtained with stereo-PIV. The particles were tracked using a polynomial predictor. As the time steps are small, and the flow is mostly bidimensional, the particles can be followed on several images, often more than 40.

# 3 RESULTS

## 3.1 Eulerian point of view

In figures 4, 5, 6 and 7, spatio-temporal diagrams representing the velocity field along a vertical line are shown. One vector over 4 is shown along Y, and one over 50 along t. The horizontal velocity component is illustrated using iso-contours, red for positive values, blue for negative ones. In figure 4, the flow is oscillating very smoothly. When the water level is increasing, the flow is slowing down, in order to keep the flow rate. In figure 5, the behaviour is rather similar. Anyway, when the bore is breaking, the velocity is going in reverse direction. In figure 6, the breaking occurs on two pseudo-periods. The boundary layer is more visible, and as the oscillations are smaller, the deceleration is less clear, except when the bore is arriving. Under the bore, there is a stagnation point near the floor. In figure 7, there is a brutal deceleration when the bore is coming. The breaking zone is large with
<figure><img src="image_7.png" /><figcaption>Figure 6: Spatio-temporal diagram of the velocity field for Fr=1.44. The vectors represent the 2D velocity field. The colours represent the horizontal velocity component.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: Spatio-temporal diagram of the velocity field for Fr=1.58. The vectors represent the 2D velocity field. The colours represent the horizontal velocity component.</figcaption></figure>

strong reverse velocities. The boundary layer thickness is increasing all the time. There is a flow reversal near the floor. As the Froude number is increasing, the W velocity component is increasing, especially above the initial water level.

## 3.2 Lagrangian point of view

The equation that governs the movement of a solid particle in a flow is the Maxey-Riley equation. If the particle is small, the Basset history term and the Faxen corrections can be neglected. The simplified non-dimensionalized equation is given in equation (2).

$$ \ddot{\mathbf{r}} = \frac{1}{\mathrm{St}} (\mathbf{u}(\mathbf{r}, t) - \dot{\mathbf{r}} - \mathbf{W} \cdot \mathbf{e}_z)) + \frac{3}{2} \mathrm{R} \frac{d}{dt} \mathbf{u}(\mathbf{r}, t) \quad (2) $$

where

$$ \mathrm{St} = \frac{(m_p + \frac{1}{2}m_f)U_f}{6\pi\mu ah} \quad (3) $$

$$ \mathrm{R} = \frac{m_f}{m_p + \frac{1}{2}m_f} \quad (4) $$

$$ \mathbf{W} = \frac{(m_p - m_f)g}{6\pi\mu a U_f} \quad (5) $$

<table><caption>Table 3: Characteristic numbers of the particles.</caption><thead><tr><th>Fr</th><th>d</th><th>h (m)</th><th>U<sub>f</sub> (m/s)</th><th>R</th><th>St</th><th>W</th></tr></thead><tbody><tr><td>1.13</td><td>50</td><td>0.118</td><td>0.353</td><td>0.625</td><td>0.0007</td><td>8.0·10<sup>-4</sup></td></tr><tr><td>1.31</td><td>50</td><td>0.094</td><td>0.665</td><td>0.625</td><td>0.0017</td><td>4.2·10<sup>-4</sup></td></tr><tr><td>1.44</td><td>50</td><td>0.073</td><td>0.567</td><td>0.625</td><td>0.0019</td><td>5.0·10<sup>-4</sup></td></tr><tr><td>1.58</td><td>50</td><td>0.143</td><td>0.871</td><td>0.625</td><td>0.0015</td><td>1.8·10<sup>-4</sup></td></tr><tr><td>1.13</td><td>300</td><td>0.118</td><td>0.353</td><td>0.625</td><td>0.026</td><td>2.9·10<sup>-3</sup></td></tr><tr><td>1.31</td><td>300</td><td>0.094</td><td>0.665</td><td>0.625</td><td>0.061</td><td>1.5·10<sup>-3</sup></td></tr><tr><td>1.44</td><td>300</td><td>0.073</td><td>0.567</td><td>0.625</td><td>0.067</td><td>1.8·10<sup>-2</sup></td></tr><tr><td>1.58</td><td>300</td><td>0.143</td><td>0.871</td><td>0.625</td><td>0.053</td><td>6.4·10<sup>-3</sup></td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>Figure 8: Comparison of the fluid and particles velocities for the case Fr=1.44 and a=300 µm. The black vectors is representing the fluid velocity field and the red ones, the particle velocities.</figcaption></figure>

St is the Stokes number, W is the settling parameter and R is the density ratio. And a is the particle diameter, µ is the dynamic viscosity of the water. Here the temperature of the water is 21°C. µ ≃ 9.79·10⁻⁴ Pa·s and ρ<sub>water</sub> ≃998 kg·m⁻³. For our case, the different values are given in table 3. The St and W values are small, hence in most cases, the particles velocities should be close to the fluid flow velocity. Anyway, as these numbers are evaluated for a characteristic velocity and a characteristic length, the values can change inside the flow.

The most critical case is Fr=1.44 and a=300 µm. Fluid velocities and particle velocities are compared in figure 8. From this figure, the velocity differences are within the experimental uncertainties. Another illustration is given in figure 9, where the blue lines are trajectories obtained tracking the big particles and the black lines are the trajectories integrated using the velocity fields. From this figure, it can be observed that the trajectories are very similar.

A visualization of the trajectories is computed using averages over 80 time steps (corresponding to 0.16 s) of the pre-processed images. The result is presented in figures 10, 11, 12 and 13. In the Fr=1.13 case, the trajectories are very smooth, except in the boundary layer, near the floor. The boundary layer is thickening when the water level is increasing. The Fr=1.31 case is rather similar, except that the bore front is slightly breaking, with a steeper front, and that the wavelength is shorter. For both cases, when the water level is maximum, the particles are slow-
<figure><img src="image_10.png" /><figcaption>Figure 9: Comparison of the fluid and particles trajectories for the case Fr=1.28 and a=300 µm. The black lines are obtained through the integration of the velocity fields and the blue lines are obtained tracking the big particles.</figcaption></figure>

ing down, and the trajectories are rising. The Fr=1.44 case is different as the bore is breaking (with a steep front) and as the amplitude of the free surface oscillations is much lower. The particles trajectories are more complex. Some of them seem to be circular, in the boundary layer, where some small vortices can be observed, and near the free surface where some big vortices seem to trap the particles for some time. In the centre of the flow, the trajectories seem to be entangled, as the water depth is the smallest used in the present experiments. The Fr=1.58 case present some similar characteristics: the bore is breaking and the flow oscillations are weak. Big structures are visible under the free surface. The trajectories are regular between the boundary layer and the structures under the free surface.

A way to analyze the flow a bit further is to investigate the stability of the trajectories. The trajectory of a point at $X_0$ at time $t_0$, is given by equation 6.

$$X(T) = \phi_{t_0}^{t_0+T} X_0 \quad (6)$$

$\phi_{t_0}^{t_0+T}$ is the flow map. The evolution of two particles at positions $X_0$ and $X_0 + \delta X_0$, initially very close ($||\delta X_0||$ very small), is given by the positions $X(t_0 + T)$ and $X(t_0 + T) + \delta X(t_0 + T)$. $\delta X(t_0 + T)$ is given by equation 7.

$$\delta X = F \delta X_0 \quad (7)$$

F is the flow map gradient. It is computed by computing the trajectories of 4 particles and using finite differences to compute the gradient. After an observation time T, the distance $l = ||\delta X||$ between the particles is given in equation (8).

$$l = \sqrt{\delta X_0 \cdot C \delta X_0} \quad (8)$$

where $C = F^*F$ is the Cauchy-Green tensor. The maximum distance $l_{max}$ is given in equation (9).

$$l_{max} = l_0 \sqrt{\lambda_{max}(C)} \quad (9)$$

where $\lambda_{max}$ is the greatest eigenvalue of the Cauchy-Green tensor (Shadden et al. (2005)). The FTLE (Finite Time Lyapunov Exponent) $\Lambda(T)$ is given in equation (10).

$$\Lambda(T) = \frac{1}{2T} \ln(\lambda_{max}(C)) \quad (10)$$

In principle, the highest particle separation in flow is exponential. In this case, the FTLE is independent of the integration time T. In the case of a simple shear, the separation is linear, hence the FTLE is decreasing with the integration time T. The FTLE fields are given in figures 14, 15, 16 and 17. The computation time is T=0.1 s. Eight fields have been stuck together to give an impression of the time evolution of the fields. The red values represent strong trajectories unstabilities, while blue values gives stable trajectories. Near the free surface, there is always strong unstabilities due to the velocity jump. Near the floor, FTLE fields are green or red, showing the presence of strong shear. Very strong shear occurs also near the breaking of the bore. In figure 14, except in the boundary layer, the trajectories are very stable. There is only a slight augmentation of the distance between two adjacent trajectories under the bore but they go back to their original configuration afterwards. In figure 15, there are more unstable trajectories. The highest values are situated where the bore is breaking. The boundary layer is thicker than for Fr=1.13. In the middle, there are still regions where the trajectories are stable. There is a thick layer also under the free surface. In figure 16, there are no more stable trajectories. As the water depth is the lowest, the boundary layer on the floor and the layer under the free surface are meeting. There is still a strong signature of the bore breaking. The last case (figure 17), there is even more energy in the bore. The breaking is strongly emphasized and its effects last for a long time. The unstable layer under the free surface goes deep in the water. The floor boundary layer is thick, but as the water depth is high, it doesn't reach the upper layer. Stable trajectories are going through the channel between the two layers.

## 4 CONCLUSION

The study of moving bores in laboratories is complementary to in-situ measurement campaigns. The big advantage is that it is possible to use very sophisticated measurement techniques to scrutinize all the specificities of this kind of unsteady flow. In this paper, stereo-PIV measurements coupled with PTV measurements have been used to show the different behaviours of the flow under the bore. For these study cases, no real local differences have been shown between the flow and the particle velocities for a range of particle diameters included between 50 to 300 µm. Moreover, the study of the trajectories and their stability gives new insights into the way that the flow is structured. The regions of potential
<figure><img src="image_11.png" /><figcaption>Figure 10: Visualizations of the trajectories under the bore front for Fr=1.13. Each line has a duration of 0.16 s.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 11: Visualizations of the trajectories under the bore front for Fr=1.31. Each line has a duration of 0.16 s.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12: Visualizations of the trajectories under the bore front for Fr=1.44. Each line has a duration of 0.16 s.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 13: Visualizations of the trajectories under the bore front for Fr=1.58. Each line has a duration of 0.16 s.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 14: FTLE field under the bore front for Fr=1.13. The integration time is $T=0.1$ s. The highest values correspond to the red color, and the lowest to the blue color.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 15: FTLE field under the bore front for Fr=1.31. The integration time is $T=0.1$ s. The highest values correspond to the red color, and the lowest to the blue color.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure 16: FTLE field under the bore front for Fr=1.44. The integration time is $T=0.1$ s. The highest values correspond to the red color, and the lowest to the blue color.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 17: FTLE field under the bore front for Fr=1.58. The integration time is $T=0.1$ s. The highest values correspond to the red color, and the lowest to the blue color.</figcaption></figure>
high impact on the sediment transport appear clearly. The Lagrangian analysis has highlighted different trajectories dependant of the Froude number and the flow structures close to the bottom. When the bore is undular, the trajectories are very stable. The only effect is a slight divergence of the trajectories under the bore. Anyway, it can have an effect on the structuration of the bed, but in the present experiment, the sediments were already in the flow. For higher Froude numbers, the impact of the bore on the flow is more dramatic. Strong vortex structures appear under the free surface, and the boundary layer is thickened, leading to the birth of new structures in the flow. These structures should have a great impact on the resuspension of the sediment. The erosion at the bottom will be the subject of further studies.

## ACKNOWLEDGEMENT

The authors would like to acknowledge the French National Agency for their financial support in the Project BLANC MASCARET 10-BLAN-0911, the FEDER and the Region Poitou-Charentes.

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