# Influence of bed roughness and megatidal current (inertial regime) on saltation

Gaspard Minster, F Floc'H, Alexandre Valance, N Le Dantec, Amandine

Nicolle, Benoit Zerr

► To cite this version:

Gaspard Minster, F Floc'H, Alexandre Valance, N Le Dantec, Amandine Nicolle, et al.. Influence of bed roughness and megatidal current (inertial regime) on saltation. Coastal dynamics 2021, Jun 2021, Delft (Virtual Event), Netherlands. [hal-04974750](https://hal.science/hal-04974750v1)

HAL Id: hal-04974750

https://hal.science/hal-04974750v1

Submitted on 3 Mar 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Influence of bed roughness and megatidal current (inertial regime) on saltation

G. Minster¹;⁵, F. Floc'h², A. Valance³, N. Le Dantec², A. Nicolle¹;⁴, B. Zerr⁵

1-ENSTA-Bretagne, 2 rue François Verny, BP 92208, 29806 Brest cedex 9, France

2-Geosciences Ocean UMR6538 UBO/IUEM Plouzané, France

3-Institut de Physique de Rennes, CNRS UMR 6251, Univ Rennes, France

4- Laboratoire Adaptation et Diversité en Milieu Marin (AD2M), UMR 7144, Roscoff, France

5-Lab-STICC, UMR CNRS 6285, Brest, France

**1. Introduction**

To maximize energy production, the hydro-kinetic turbines are generally installed in marine environment with extreme tidal currents. Under these conditions, coarse sediment with diameter greater than a few centimeters can be transported by the flow whereas in standard marine environment they are considered as immobile sediment. The study of particle transport in the context of strong current is the purpose of this paper. In the present work, we conducted experiments to study saltation motion with large particles in the regime of high particle Reynolds number ranging from 1000 to 5000, and on fixed beds with varying roughness. This provides unusual experimental conditions in comparison with the literature. In our study, different bed roughnesses, particles diameter and flow speed were used. Our aim is to study saltation motion in flow regimes that mimic macro-tidal environments and to propose laws allowing to estimate the jump height and length in such extreme regimes.

**2. Methods**

Experiments were carried out in a free-surface flume (40 cm wide, 60 cm height and 500 cm long). The flume is equipped with two pumps able to produce a flow discharge of 60 l/s. A honeycomb structure was set at the beginning of the flume in order to break the large turbulent structures. Bed roughness is made with spherical particles of uniform diameter dB glued on steal plates placed at the bottom of the channel. The particles are highly packed according to a random arrangement (non-crystalline structure). Three different flow rates (11, 25 and 45 l/s), three different bed roughnesses (dB=1.2, 1.6 and 2.6 cm) and three different particle diameters (d=1.6, 3 and 5 cm) are tested. The roughness length ks and the shear velocity u* were determined using the logarithmic fit of velocity profile data. The particles are tracked within a vertical plane parallel to the main flow direction thanks to a fast video camera (FastCam Photron Mini) recording 500 frames per seconds with a resolution of 1280x400 pixels.

**3. Results and discussion**

After having shown that the critical Shields number decreases with decreasing relative bed
roughness (Fig 1.a), we analyzed the particle trajectory in terms of jump height and length and also
characterized the main features of the impact of the saltating particle on the rough bed. Significant
changes are observed in the characteristics of the particle trajectories according to the relative bed
roughness (Fig 1.c and 1.d). Interestingly, our data indicate that both the jump height and length
increase with increasing bed roughness (Bhattacharyya et al., 2013). However, in contrast with the
latter study where they found that the aspect ratio of the trajectory H=L is almost invariant with
the bed roughness, our results reveal that the aspect ratio increases significantly with the relative
bed roughness (from 0.1 to 0.25). These differences may be explained by the fact that our
experimental conditions lie in the regime of high Stokes numbers (St = 5.10⁴) where the role of
viscous dissipation in collisions is expected to be marginal. This result seems to confirm the
important role of the collision process in the saltation motion. Importantly, we also found that the
jump height rescaled by the bed roughness dB obeys a unique power law with the excess shear
(Fig. 1.c). The effect of the bed roughness is taken into account both through the critical Shields
parameter and via the proportionality of the jump height with the bed roughness. This result differs
from previous studies (Sklar & Dietrich, 2004; Auel et al., 2017) which consider the particle
diameter as the relevant scaling parameter. Additionally, we analyzed the key features of the
collision process, including the impact angle and the dissipation in the impact. The mean impact
angle is closely related to the bed roughness: an increase of the relative bed roughness leads to an
increase of the mean impact angle, from 19.5° to 32.6° for dB/d = 0.3 and 1.2, respectively (Fig. 1.b). First, for a given bed roughness, the vertical restitution coefficient (which is the ratio of the vertical rebound velocity to the vertical impact velocity) is a decreasing function of the impact angle and reaches values greater than 1 for grazing impacts, as observed in aeolian saltation transport (Beladjine et al., 2007; Berzi et al., 2016). Second, for a given impact angle, the vertical restitution coefficient is found to increase with increasing bed roughness. As a result, the optimum impact angle for sustained saltation is decreased as the bed roughness increases, as observed in our experiments. A parallèle is then possible with conclusions made for bed slope influence on saltation motion (Ancey et al., 2002).

<figure><img src="image_2.png" /><figcaption>Figure 1. a) Saltation threshold versus relative bed roughness. b) Mean rebound angle as a function of the mean impact angle. c) Dimensionless mean jump height and d) Dimensionless mean jump length as a function of the excess shear stress.</figcaption></figure>

## Acknowledgements

The work was supported by the ANR FEM project PHYSIC ANR-10-IEED-0006-10. G.M. is particularly grateful to the IPR team for their help during the laboratory experiments.

## References

* Ancey, C., Bigillon, F., Frey, P., Lanier, J., & Ducret, R. 2002. Saltating motion of a bead in rapid water stream. *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 66(3), 1-16.

* Auel, C., Albayrak, İ., Sumi, T., & Boes, R. M. 2017. Sediment transport in high speed flows over a fixed bed: 1. particle dynamics. *Earth Surface Processes and Landforms*, 42(9), 1365-1383.

* Beladjine, D., Ammi, M., Öger, L., & Valance, A. 2007. Collision process between an incident bead and a three-dimensional granular packing. *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 75(6), 1-12.

* Berzi, D., Jenkins, J. T., & Valance, A. 2016. Periodic saltation over hydrodynamically rough beds: aeolian to aquatic. *Journal of Fluid Mechanics*, 786, 190-209.

* Bhattacharyya, A., Ojha, S. P., & Mazumder, B. S. 2013. Evaluation of the saltation process of bed materials by video imaging under altered bed roughness. *Earth Surface Processes and Landforms*, 38(12), 1339-1353.

* Sklar, L. S., & Dietrich, W. E. 2004. A mechanistic model for river incision into bedrock by saltating bed load. *Water Resources Research*, 40(6), 1-22.