# Individual and collective plants motion in a submerged, staggered, flexible, artificial canopy

L. Guiot, D. Doppler, J. John Soundar Jerome, B. Löhrer, J. Fröhlich, N. Riviere

► To cite this version:

L. Guiot, D. Doppler, J. John Soundar Jerome, B. Löhrer, J. Fröhlich, et al. Individual and collective plants motion in a submerged, staggered, flexible, artificial canopy. River Flow 2022, the 11th International Conference on Fluvial Hydraulics, Ana Maria Ferreira da Silva, Colin Rennie, Susan Gaskin, Jay Lacey, Bruce MacVicar, Nov 2022, Ottawa (Canada), Canada. pp.781-785, 10.1201/9781003323037-105. [https://doi.org/10.5016/c66](https://doi.org/10.5016/c66)

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# Individual and collective plants motion in a submerged, staggered, flexible, artificial canopy

L. Guiot

Université de Strasbourg, CNRS, ENGEES, Icube, Strasbourg, France

D. Doppler & J. Soundar Jerome

LMFA, INSA Lyon, UCBL, ECL, Université de Lyon, Villeurbanne, France

B. Löhrer & J. Fröhlich

Institute of Fluid Mechanics, Technische Universität Dresden, Germany

N. Riviere

LMFA, INSA Lyon, UCBL, ECL, Université de Lyon, Villeurbanne, France

**ABSTRACT:** This study deals with aquatic canopies and their interaction with an open-channel flow. It focuses on individual and collective plant motion in a staggered, submerged, flexible canopy. The study is based on experiments performed within a 2 m long canopy composed of 330 flexible blades. The individual motion of four blades, marked with fluorescent spots, is monitored with a video camera. A series of experiments are performed at 13 different values of the Cauchy number (between 1 and 200). Four canopy motion patterns are present in a non-aligned flexible canopy: Rigid (blades do not move), Swaying (blades bend back and forth not forming an organized pattern), Monami (blades are significantly deflected and a coherent waving motion is observed), and Prone (blades bend over, permanently). Comparison with a previous study of aligned canopy motion shows that the Cauchy number is a key parameter to delimit these four regimes.

## 1 INTRODUCTION

Canopies are a fundamental element of aquatic ecosystems, as the fluid-structure interaction between the flow and the flexible plants determines hydraulics as well as transport of sediment, nutrients and pollutants. Okamoto et al. (2016) studied this interaction in a submerged canopy made of flexible, rectangular blades aligned with the channel banks. They identified four types of motion: Rigid (blades do not move), Swaying (blades bend back and forth not forming an organized pattern), Monami (blades are significantly deflected and a coherent waving motion is observed), and Prone (blades bend over, permanently). These patterns of motion could be controlled and reinforced by the alignment of the blades. The objective of the present work is to study the dynamics of several different blades in a staggered canopy to see if there are collective motions similar to those observed in a canopy with aligned blades, i.e. channeling between the blades.

## 2 MATERIAL AND METHOD

### 2.1 Artificial canopy and hydraulic condition

A 2 m long, flexible canopy was installed in a 25 cm wide and 7 m long, tilting open channel. It consists of blades (6 cm high, 2 cm wide, and 0.1 mm thick blade) with a density of 1.9 $10^3$ kg/m$^3$ and a stiffness modulus equal to 3.78 GPa. The canopy layout has 66 rows of 5 blades, spaced 3 cm apart in the streamwise direction (Fig. 1). The vegetation density $a$, defined as the total frontal area per unit canopy volume, is equal to $13.2 m^{-1}$. Experiments were performed at a constant water height $h = 18$ cm, i.e. three times the blade height. The flow rate was varied to obtain 13 different mean flow velocity values (between 10 cm/s and 68 cm/s). This flow velocity variation yields a variation of the Cauchy number, the ratio of the drag force applied to a blade by the flow and the blade elastic force, here defined as

$$Ca = \frac{c_d \rho U_{fc}^2 w_b h_b^3}{2EI}, \qquad (1)$$
where $C_d$ is the blade drag coefficient, $U_{tc}$ the water velocity flow at the top of the canopy, $\rho$ the fluid density, $h_b$ the blade height, $w_b$ the blade width, $E$ the blade stiffness modulus, and $I$ is the blade second moment of area (for a rectangular blade $I = w_b e_b^3/12$ with $e_b$ the thickness of the blade). In this study, the hydraulic conditions led to Cauchy numbers between 1 and 200.

<figure><img src="image_2.png" /><figcaption>Figure 1. Experimental setup: a) Canopy schematic top view, b) picture of blade in the flow, six blades were initially painted but due to lack of space along the open-channel only four blades are visible by the camera, c) and photography, showing the test-pattern, of the four blades used for image analysis.</figcaption></figure>

## 2.2 Experimental setup and measurement techniques

To follow the motion of the blades, a technique allowing to sort these motions within the canopy was developed. The free ends of four selected blades were marked with fluorescent paint and illuminated with ultraviolet light, coping with other blades passing in front of the camera. Films were made at a frequency of 20 Hz over a duration of 6 min 49 sec. These four blades are located in successive rows, aligned along the streamwise flow direction, with a crosswise offset of 5 cm due to the staggered layout (Fig. 1). They are numbered from 1 to 4 from upstream to downstream. Blade n°1 is located 1.22 m downstream the canopy edge. These blades were selected in order to detect a global behavior of the canopy, i.e., if the movements of the 4 blades have the same characteristics, or if there is a creation of locally correlated movements characterized by the appearance of a behavior differing from blade to blade.

The same image processing was applied to the monochromatic films obtained by extracting the red and green channels, using ImageJ® software, namely a thresholding to highlight color paint marks and de-speckling to remove some spatial noise. Figure 2 depicts examples of the results: the instantaneous deflection (vertical position $y(t)$ of the blade top) for the four marked blades.

# 3 RESULTS AND DISCUSSION

## 3.1 Cross correlation of blades

The cross-correlation function of the vertical positions $y(t)$ of the tips of the blades is used to monitor the correlation of their motions. Figure 3 shows a large correlation between blades 3 and 4, and this is consistent with their instantaneous deflected heights in figure 2. Between these two blades, a correlation greater than 0.8 is observed for all the mean flow velocity values tested, except for the lowest. The correlation decreases when increasing the inter-blade distance – it is always smaller than 0.4 between blades 1 and 3 that are 1.5 blade height apart (Fig. 3b) – but remains visible. The clearly observable correlation peak provides the lag time between the motion of different blades. This lag time obviously decreases as the inter-blade distance decreases (Fig.3-a) or as the mean flow velocity increases (Fig.3-c). In figure 3-b, an increase in correlation between the motion of two blades separated by 1.5 blade heights is visible for a mean flow velocity equal to 0.3 m/s.
<figure><img src="image_3.png" /><figcaption>Figure 2. Evolution of instantaneous deflected height for mean flow velocity equal to 0.44 m/s.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3. Cross correlation of instantaneous deflected heights for a mean flow velocity 0.44 m/s a) correlation between blade n°1 and n°4 (two blade heights apart), blade n°1 and n°3 (1.5 blade heights apart), blade n°2 and n°3 (1 blade height apart), and blade n°3 and n°4 (0.5 blade heights apart), b) change of maximum correlation with flow velocity, c) change of the lag time between blade n°1 and n°3 with flow velocity.</figcaption></figure>

## 3.2 Blade deflection

The mean and the standard deviation of the instantaneous deflection of blade n°4 are shown in Figure 4a and 4b, respectively, as a function of the mean flow velocity. To compare with literature data, these results are plotted in a dimensionless form in Figure 4c, were the reconfiguration $R$ is plotted as a function of the Cauchy number, along with data from Okamoto et al. (2016) for comparable canopy and flow conditions: vegetation density is $a = 7.1 \text{ m}^{-1}$, blades dimensions are $5 \text{ cm} < h_b < 10.5 \text{ cm}$, $w_b = 8 \text{ mm}$, and $e_b = 0.1 \text{ mm}$. Comparing these data is not easy because various different definitions exist for the Cauchy number, in particular concerning the choice of the flow velocity and the value of the drag coefficient. For the present data, the velocity $U_{tc}$ is calculated with the lag time and the distance between two blades, and we consider a fixed value $C_d = 2$ (value for an isolated, rectangular, thin plate). For data from Okamoto et al. (2016), owing to the blade material, similar to Velasco et al. (2003), we considered as Young modulus 2.38 GPa. $U_{tc}$ is estimated introducing the reported shear velocities in the velocity profile of Niskora et al. (2013) and considering $C_d = 2$.

Four patterns of blade motion are visible. No deflection at the lowest mean velocity, $y(t)$ is almost constant, with a quasi-null standard deviation and $R \approx 1$. This is consistent with the low value of the Cauchy number, where drag does not overcome the blade stiffness. For higher velocities, in the range 0.15-0.25 m/s, the deflection remains low but the standard deviation of the deflection increases with $U_{tc}$ (Fig.4-a). The motion of (very) close blades (separated by less than one blade height) are strongly correlated. This corresponds to the “swaying” behavior proposed by Okamoto et al. (2016) which in the present study occurs for smaller $Ca$ compared to this reference. For higher velocities, in the range 0.3-0.45 m/s, both deflection ($R$ decreases) and standard deviation of the deflection increase. The motion of more distant blades, one or two blade heights apart, is correlated, with an increased correlation coefficient. This pattern corresponds to Monami. Fig 4-c shows that its appearance agrees with the experiments in the literature. Finally,
for the highest velocities, above 0.5 m/s, the deflection increases but the standard deviation remains constant. This corresponds to the “prone” regime, for high Ca values (Fig 4-a), in agreement with literature data. The absence of flow corridors achieved by the staggered arrangement of blades in the present configuration does not modify the patterns of motion of the blades. Hence, their coordinated motion in a submerged canopy is not due to a particular arrangement of the blades. The relevance of the Cauchy number to classify these patterns is confirmed. Only a slight modification of the onset of these patterns with the Cauchy number value is suggested. For other blade characteristics, the points are somewhat shifted in the (Ca, R) plane; this suggests an influence of the blade length.

<figure><img src="image_5.png" /><figcaption>Figure 4. Statistics of blade deflection for blade n°4: a) mean, the red dot-dashed line indicates an inflection in deflected height decrease, b) standard deviation of deflection, the blue dashed line indicates a stop of the increase in the standard deviation, c) reconfiguration R (ratio of the mean deflected height by blade height) as a function of the Cauchy number Ca: present data with crosses data from Okamoto et al. (2016) in closed symbols (blades of length $h_b$ = 5 cm) and in open symbols (other blades with $h_b$ ≥ 7 cm).</figcaption></figure>

# 4 CONCLUSIONS

These experiments on a staggered canopy show the limited role of the canopy organization on the blade motion. They also emphasize the difficulty in comparing different existing datasets, because of the computation of the Cauchy number according to available flow characteristics. Further work is required (i) to determine the most relevant flow velocity for the Cauchy number, (ii) to find a relationship between the drag coefficient of the blades and their arrangement, (iii) to assess the role of the ratio between the characteristic lengths of the flow and of the blades.

# ACKNOWLEDGEMENTS

This work was funded by the French-German ANR-DFG project ESCaFlex (ANR-16-CE92-0020, DFG grant 634058).

# REFERENCES

* Nikora, N., Nikora, V., & O'Donoghue, T. 2013. Velocity profiles in vegetated open-channel flows: combined effects of multiple mechanisms. *Journal of Hydraulic Engineering, 139*(10), 1021-1032.

* Okamoto, T., Nezu, I., & Sanjou, M. 2016. Flow-vegetation interactions: length-scale of the “monami” phenomenon. *Journal of Hydraulic Research, 54*(3), 251-262.

* Velasco, D., Bateman, A., Redondo, J., & Demedina, V. 2003. An open channel flow experimental and theoretical study of resistance and turbulent characterization over flexible vegetated linings. *Flow, Turbulence and Combustion, 70*, 69-88.