Philippe Mercier
email: philippe.mercier@unicaen.fr

Maxime Thiébaut

Sylvain Guillou
email: sylvain.guillou@unicaen.fr

Christophe Maisondieu

Emmanuel Poizot

Aline Pieterse

Jérôme Thiébot

Jean-François Filipot

Mikaël Grondeau

Thiébaut Maxime

Guillou Sylvain

Maisondieu Christophe

Poizot Emmanuel

Pieterse Aline

Thiébot Jérôme

Filipot Jean-Francois

Grondeau Mikaël

Turbulence measurements: An assessment of Acoustic Doppler Current Profiler accuracy in rough environment

Keywords: Turbulence, Lattice Boltzmann Method, Large-Eddy Simulation, ADCP, Environmental flows

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Introduction

Tidal power constitutes a potential new source of low carbon power. Although the tidal industry is still in a development phase, real scale prototypes are being tested in operating conditions (e.g., Simec Atlantis and Andritz Hydro turbines in the Pentland First, Sabella turbine in Passage du Fromveur, Hydroquest turbine in Paimpol-Bréhat). As tidal power farms will be composed of arrays of devices distributed over relatively large areas, the optimal layout will depend, for a large part, on the characteristics of the hydrodynamics and the variability of the flow in time and space. Regional tidal flow simulations provide accurate estimates of flow intensity and direction [START_REF] Thiébot | Wake field study of tidal turbines under realistic flow conditions[END_REF]; [START_REF] Lewis | Resource assessment for future generations of tidal-stream energy arrays[END_REF]; [START_REF] Thiébaut | Merging velocity measurements and modeling to improve understanding of tidal stream resource in Alderney Race[END_REF]]. However, these studies are based on Reynolds averaged numerical simulations, that only resolve the time-mean flow and model the effect of turbulence. Although they allow for estimating the turbulence intensity [Togneri et al. (2017b)], they do not simulate turbulent eddies and are limited in terms of spatial and temporal resolutions. Following the work of [START_REF] Finnegan | Operational fatigue loading on tidal turbine blades using computational fluid dynamics[END_REF]], four main aspects have been identified that contribute to unsteady loads on tidal turbine blades and their premature fatigue: the cyclic loading of a blade linked to the vertical gradient of velocity in the swept area, the shadow effects from the support structure, the force due to the sea surface waves [START_REF] Lewis | Realistic wave conditions and their influence on quantifying the tidal stream energy resource[END_REF]] and the force due to ambient turbulence. As incoming turbulence is an important source of mechanical constraints on tidal turbines [Thiébaut et al. (2020b); [START_REF] Milne | The characterisation of the hydrodynamic loads on tidal turbines due to turbulence[END_REF]] and impacts turbine wakes [START_REF] Grondeau | Wake of a ducted vertical axis tidal turbine in turbulent flows, LBM actuator-line approach[END_REF]], its characterisation is essential [START_REF] Milne | The characterisation of the hydrodynamic loads on tidal turbines due to turbulence[END_REF]]. The power production is stable over long periods of time [START_REF] Lewis | Power variability of tidal-stream energy and implications for electricity supply[END_REF]], however, turbulence might generate electrical surges that need to be anticipated to preserve the power system. Several Large-Eddy Simulations (LES) have been performed, such as [START_REF] Zangiabadi | Computational fluid dynamics and visualisation of coastal flows in tidal channels supporting ocean energy development[END_REF]] in the Ramsey Sound, [START_REF] Bourgoin | Turbulence characterization at a tidal energy site using large-eddy simulations: case of the Alderney Race[END_REF]] and [Mercier et al. (2020a)] in the Raz Blanchard, and [START_REF] Le | Large-eddy simulation of the Mississippi River under base-flow condition: hydrodynamics of a natural diffluenceconfluence region[END_REF]] in the Mississippi River. These simulations enable the assessment of turbulence metrics, such as the full Reynolds tensor, but are limited in resolution, temporal and spatial coverage.

In situ measurements are widely used to estimate the local turbulence metrics [Thomson et One of the main limitations of ADCPs when it comes to turbulence characterisation is the assumption of the homogeneity of the flow field over the measurement volume. Indeed, such sensors use beams that diverge away from the sensor. Hence, the volume in which the flow is assumed homogeneous and in which the measurements are being integrated, increases, changing the spatial averaging of the flow characteristics. Although this homogeneity assumption is widely applied, its validity is likely to fail in particular flow conditions.

An analytical study of the ADCP functioning allows to assess their limits [START_REF] Guion | The frequency response of acoustic doppler current profilers: Spatiotemporal response and implications for tidal turbine site assessment[END_REF]].

However, such an analysis does not take into account the specificity of a realistic flow field, and in particular the potential spatial variability of the flow characteristics. The validity of ADCP data processing can be assessed through Virtual-ADCP (V-ADCP) methods, which consists in applying ADCP data processing to a controlled flow field generated analytically [START_REF] Crossley | Quantifying uncertainty in acoustic measurements of tidal flows using a 'Virtual' Doppler Current Profiler[END_REF]] or by numerical simulation [START_REF] Tokyay | Investigation of two elemental error sources in boat-mounted acoustic Doppler current profiler measurements by large eddy simulation[END_REF]; [START_REF] Richmond | Numerical performance analysis of acoustic Doppler velocity profilers in the wake of an axial-flow marine hydrokinetic turbine[END_REF]]. The velocity field should be representative of the studied environmental flow. In particular, the impact of realistic rough seabed morphology on the turbulent characteristics and on the related accuracy of the data processing method has not, to the authors' knowledge, been addressed yet.

The seabed roughness is known to impact the flow characteristics [START_REF] Hama | Boundary-layer characteristics for smooth and rough surfaces[END_REF]; [START_REF] Schlichting | Boundary layer theory[END_REF]; [START_REF] Schindler | The environmental hydraulics of turbulent boundary layers, chapter 5[END_REF]]. The structure of flows over a rough seabed is characterised by a rough sub-layer, in which individual roughness wakes induce three-dimensional variations in the flow characteristics. The thickness of this layer is typically two to five time the roughness height [START_REF] Nikuradse | Laws of flow in rough pipes[END_REF]; [START_REF] Perry | Rough wall turbulent boundary layers[END_REF]], in such a way that in high seabed roughness areas, ADCP measurement validity could be questioned in a large part of the water column. A specific study of the rough sub-layer and its impact on ADCP measurement accuracy in typical tidal power flows is thus necessary.

The structure of environmental flows can be addressed through canopy flow studies, in which roughness is represented by macro-roughness distributions. Uniform distributions of wall-mounted cubes have been investigated experimentally by [Florens et (2020b)] experimentally and numerically investigated the flow over combinations of real seabed elements such as big rocks or abrupt changes of seabed elevation. However, these studies are limited to moderate Reynolds numbers (Re ≈ 10 6 ), which is not representative of flows at tidal energy sites (Re ≈ 10 8 ). To conduct numerical simulations at high Reynolds number, the choice of the numerical method is crucial to handle large and complex simulation domains. The Lattice Boltzmann Method (LBM) is an unsteady computational fluid dynamic method based on the resolution of the Boltzmann equation [START_REF] Bhatnagar | A model for collision processes in gases[END_REF]; [START_REF] Qian | Lattice BGK models for Navier-Stokes equation[END_REF]]. It is well suited to large and complex geometries [START_REF] Succi | Three-dimensional flows in complex geometries with the lattice Boltzmann method[END_REF]] and can be combined with LES [START_REF] Smagorinsky | General circulation experiments with the primitive equations[END_REF]; [START_REF] Eggels | Numerical simulation of free convective flow using the lattice-Boltzmann scheme[END_REF]] in order to resolve a large part of the turbulence energy spectrum and to investigate the motion of the largest eddies [START_REF] Sagaut | Large Eddy Simulation for Incompressible Flows[END_REF]] (those that contain most of the turbulent energy and control most of the momentum transfer and turbulent mixing).

For these reasons, LBM-LES has been used for environmental numerical simulations [START_REF] Parmigiani | A lattice Boltzmann simulation of the Rhone river[END_REF];

Mercier et al. (2020a)].
Here, LBM-LES is chosen to perform a simulation of a channel flow over a uniform distribution of wallmounted cubes, designed to be representative of a tidal energy site. The V-ADCP method is performed on the simulation output to test the accuracy of the ADCP configuration proposed by [START_REF] Vermeulen | Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows[END_REF]]. Firstly, the numerical simulation method is presented, as well as the ADCP configuration and principles of the V-ADCP method. Then, the simulation results are exploited to investigate the sources of error. Finally, the prospects and limits of the method are discussed.

Methods

Numerical flow simulation

Simulations are performed with the LBM [START_REF] Bhatnagar | A model for collision processes in gases[END_REF] The seabed is composed of 3 m-large cubic elements disposed regularly over the bottom (see Figure 1). This macro-roughness aims at generating a vertical variation of the turbulence intensity similar to that measured with two, coupled, 4-beam ADCPs in the Raz Blanchard [Thiébaut et al. (2020b)], where the mean vertical profile of longitudinal turbulence intensity ranged from 12% near the surface to 21% near the ADCPs at the seabed.

As the domain is periodic, the load losses tend to decrease the flow velocity. This effect is offset by a longitudinal volume force that sustains the flow. The time step is 0.010 s. The mesh resolution is 0.21 m near the seabed and 0.42 m near the water surface. The domain contains 28.3 million cells. The average longitudinal speed is 3 m.s -1 for a volume force corresponding to a 2.5×10 -3 m.s -2 acceleration.

The instantaneous longitudinal velocity along a vertical longitudinal plane is shown in Figure 2. The simulation ran on 56 processors for 78 h. The total simulated time is 52 min, with a convergence period of 36 min. For in situ measurements, the period of data extraction must be long enough to guarantee a sufficient number of samples, and short enough not to be affected by changes in the hydrodynamic conditions relative to the tidal cycle. This condition is satisfied by using a 10 min period in the case studied in the work of [Thiébaut et al. (2020b)]. Here, as there is no variation in the hydrodynamic conditions, the period is extended to 16 min. Longitudinal, lateral and vertical velocity components are respectively referred to as u, v and w, acting in the x, y and z directions. Herein, time averaged (u) and time fluctuating (u ) velocities are defined in such way that u = u + u .

Virtual-ADCPs

In the present work, the two, coupled, 4-beam ADCP configuration designed by [START_REF] Vermeulen | Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows[END_REF]] is tested. This configuration is specially conceived for turbulence measurements. Its working principle is described hereinafter. The V-ADCPs are modelled to represent the sampling geometry of the coupled ADCPs in the representative velocity field derived from the numerical flow simulation. Two upward-looking 4-beam V-ADCPs coupled in a master-slave set-up, are positioned on the seabed forming an 8-beam arrangement where the beams are numbered from 1 to 8 (Figure 3). The two V-ADCPs are at a distance of 0.5 m from each other. The V-ADCPs record alternatively the velocities in beam coordinates is defined relative to the master V-ADCP, with the origin O located at the centre of the four transducers (Figure 3). The orientation of the master V-ADCP is such that the opposite beams 1 and 2 are oriented along the direction of the longitudinal velocity u, defining the x-axis, whereas beams 3 and 4 are oriented along the direction of the lateral velocity v, defining the y-axis. The slave V-ADCP is rotated to an angle φ 1 = 20˚around the x-axis (Figure 3), and φ 3 = 45˚around the z-axis resulting in a tilted V-ADCP with one beam pointed vertically upward (Figure 4). No rotation is applied around the y-axis (φ 2 = 0˚).

The coupled ADCP method, developed by [START_REF] Vermeulen | Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows[END_REF]], combines (i) the traditional transformation method, where two opposite beams of the ADCP are used to transform velocities in beam coordinates to velocities in Cartesian coordinates, with (ii) the rotation of the slave relative to the master ADCP. The velocities in beam coordinates equates to the velocities (u, v, w) in Cartesian coordinates as in Equation 1:

b = T.u ( 1
)
where b is an eight-component vector containing all the radial velocity components from the two coupled ADCPs, u is the velocity vector in the Cartesian coordinate system (u = u e x + v e y + w e z ) and 2:

T
v b = Q.r (2)
The six-element vector r can be rearranged to form the Reynolds stress tensor according to Equation 3:

r =    r 1 r 4 r 5 r 4 r 2 r 6 r 5 r 6 r 3    =    u 2 u v u w u v v 2 v w u w v w w 2   
(3) The Reynolds stresses indicate the orientation of the eddies in the flow and are often used to estimate fundamental turbulence metrics such as the turbulence intensity, the TKE dissipation rate or the TKE production rate. Here, the u u , v v and w w components will be referred to as normal stresses and the u v , u w and v w components as the shear stresses.

V-ADCP cells are defined by all the mesh nodes included in a volume delimited by a frustum of 4 • beam cone. The cells of the master and slave V-ADCP are respectively 1.28 m and 1.37 m thick. This corresponds to the configuration used in [Thiébaut et al. (2020c)]. The cells are presented in Figure 4.

They are composed of a number of mesh nodes ranging from 4 to 135 and their volume ranges from 0.5 m 3 to 17 m 3 , depending on their elevation. Similarly to real ADCPs, the spatial averaging of the radial velocity is performed on each cell volume. This process is replicated on each V-ADCP beam. The issue of Doppler noise [START_REF] Brumley | Performance of a broad-band acoustic Doppler current profiler[END_REF]] and other practical operational considerations are ignored. Also, if the acquisition frequency affects the consideration of the smallest scales of the turbulence in standard ADCP uses [START_REF] Guion | The frequency response of acoustic doppler current profilers: Spatiotemporal response and implications for tidal turbine site assessment[END_REF]], it is not the case for data processing based on the variance method.

Thus, this matter is not addressed here.

The Reynolds stresses are computed directly from the synthetic flow field on a vertical profile centred on the master V-ADCP position, with a high frequency data acquisition (100 Hz). This dataset will be referred to as the reference dataset. Simultaneously, the Reynolds stresses are calculated from the velocities recorded by the V-ADCP. The comparison between Reynolds stresses derived from both methods will allow for the assessment of the error inherent to ADCP measurements.

Results

Comparison of Reynolds stresses derived from the reference dataset and V-ADCP

Figure 5 shows scatterplots of the six components of the Reynolds stress tensor derived from the reference dataset and the V-ADCP at each cell elevation. The 1:1 black line indicates perfect agreement between Reynolds stresses derived from both methods.

In general, a good agreement is found, with the u u , v v , w w , u v and u w components matching the 1:1 line. However, a few values are found to be significantly far from the 1:1 line, especially in the normal stresses u u and v v , where these values were calculated near the seabed. Moreover, the component v v exhibits some inconsistencies with two negative values derived from the V-ADCP.

The scatterplots of the normal stresses (u u , v v and w w ) are slightly right-skewed, indicating that the V-ADCP underestimates these components. Since the normal stresses allow for the calculation of the turbulence intensity, it is expected that the V-ADCP gives underestimated values of this metric.

Moreover, the shear stress, v w , is characterised by very low absolute values. This is imputed to the symmetric characteristic of the domain. The domain symmetry should imply that the u v component also satisfies this condition, which is not the case. Vertical profiles of the Reynolds stresses are shown in Figure 6. This figure exhibits a good agreement between profiles derived from the reference dataset and V-ADCP. The absolute error is greater near the seabed, which could result from spatial heterogeneity of the flow over a horizontal plane that invalidates the homogeneity assumption. This assumption is necessary for the application of the method proposed by [START_REF] Vermeulen | Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows[END_REF]] (Section 2.2). However, as demonstrated by [START_REF] Nikuradse | Laws of flow in rough pipes[END_REF]; [START_REF] Perry | Rough wall turbulent boundary layers[END_REF]], this assumption is true for elevations above 2 to 5 times the roughness height. Therefore, it may not be valid in the lower part of the water column, which induces high error. This is consistent with the high absolute error observed here up to 8 m above the seabed.

0 0.1 0.2 0.3 0 0.1 0.2 0.3 u u Ref erence (m 2 .s -2 ) u u V -ADCP (m 2 .s -2 ) (a) u u 0 0.1 0.2 0 0.1 0.2 v v Ref erence (m 2 .s -2 ) v v V -ADCP (m 2 .s -2 ) 10 20 30 Elevation (m) (b) v v 0 0.5 1 •10 -1 0 0.5 1 •10 -1 w w Ref erence (m 2 .s -2 ) w w V -ADCP (m 2 .s -2 ) (c) w w -0.1 0 0.1 -0.1 0 0.1 u v Ref erence (m 2 .s -2 ) u v V -ADCP (m 2 .s -2 ) (d) u v -6 -4 -2 0 •10 -2 -6 -4 -2 0 •10 -2 u w Ref erence (m 2 .s -2 ) u w V -ADCP (m 2 .s -2 ) (e) u w -1 0 1 •10 -2 -1 0 1 •10 -2 v w Ref erence (m 2 .s -2 ) v w V -ADCP (m 2 .s -2 ) (f) v w
The maximum relative error (MaxError -Equation 4) and the root mean square error (RMSE -Equation 5) between the Reynolds stresses derived from the reference dataset and the V-ADCP are shown in Table 1. Only values calculated at a height above seabed higher than 8 m are taken into account. The maximum RMSE is associated with the shear stress v w with a value of 137 %. This high value is not troublesome as the v w component is centred on zero. The RMSE of the five other components of the Reynolds stress tensor is relatively low, with values ranging from 8 % to 14 % and up to 33 % for u v .

u v (m 2 .s -2 ) Elevation (m) -5 0 •10 -2 10 20 30 (e) u w (m 2 .s -2 ) -1 0 1 2 •10 -2 10 20 30 (f) v w (m 2 .s -2 )
Figure 6: Vertical profiles of the Reynolds stresses derived from the reference dataset (blue -) and the V-ADCP (red -). Black profiles (-) denote the difference between the Reynolds stress estimation from both methods. The maximum relative error varies over a wide range, with the three components, u u , v v and w w associated with maximum relative error lower than 27 % whereas the u v and u w components exhibit maximum values of 91 % and 34 % respectively. The component, v w reveals considerable maximum error reaching 353 %, which is, once again, explained by the fact that the v w component is centred on zero.

u u v v w w u v u w v w

MaxError(X) = 100 max(|X ref -X V -ADCP |) max(|X ref |) (4) RMSE(X) = 100 Ω (X ref -X V -ADCP ) 2 L dω max(|X ref |)
(5)

Assessment of turbulence homogeneity over the beams

The operating principle of the coupled 4-beam ADCP system requires the inherent assumption of homogeneity in the flow within the sampled area. The reference dataset computed from the synthetic flow field allows for the direct determination of the vertical evolution of the Reynolds stresses along each beam of the V-ADCPs (Figure 7). It is thus possible to perform a turbulence homogeneity test over the beams.

Figure 7 shows that, for a given component of the Reynolds stress tensor, the profiles derived from each V-ADCP beam have the same behaviour. Their magnitude increases abruptly up to an elevation of 8-10 m and decreases above 10 m up to the maximum elevation. The only component that confirms the turbulence homogeneity assumption throughout the water column is the normal stress w w . For the components v v and u w the assumption is not valid for elevations higher than 15 m and 20 m, respectively. The normal stress, u u reveals two ranges in elevation where the homogeneity assumption may be validated: (i) -from 0 to 8 m and, (ii) -from 20 to 38 m (the maximum elevation). Between both layers, the Reynolds stress profiles can be split into three groups of beams. The first group is composed of beams 1, 2, 5 and 7, where these beams are aligned with the flow direction. In this direction, the turbulence is homogeneous and rapidly advected. The second group is composed of beams 4, 6 and 8, whose associated profiles exhibit similar behaviour. These beams share the same three-dimensional spanning area (Figure 4). Thus, as expected, these beams capture comparable turbulence processes.

Beam 3 spans a different area and constitutes the last group. This decomposition in three groups is particularly noticeable for the component u v , throughout the water column.

Figure 8a shows the vertical profiles of the Reynolds stresses derived from the reference dataset and averaged over the 8 beams. The profiles used to calculate and normalise the average gap between individual and spatially averaged beams are represented in Figure 8b. For u u , v v , w w and u w components, the discrepancies are high in the lower part of the water column (up to 10 m), low in the medium part of the water column and increase between 20 m and the maximum elevation. For u v and v w the same tendency is observed but with higher magnitudes. The origin of the discrepancies in the lower part of the water column can be explained by the presence of seabed roughness that is expected to affect the homogeneity of the flow up to 2 to 5 times its height (6 m to 15 m). Discrepancies observed in the upper part of the water column could be explained by increasing distance between V-ADCP beams, potentially reducing the validity of the assumption made on the horizontal homogeneity of the flow.

Effect of spatial averaging inside V-ADCP cells

Similarly to real ADCPs, the velocities derived from the V-ADCPs were averaged over each bin cell volume. This spatial averaging is expected to filter small eddies, thus affecting the evaluation of turbulence metrics. This filtering effect can be assessed through numerical simulation, because the full velocity vector is accessible at a high spatial resolution. In order to investigate the potential filtering-induced biases when characterising turbulence, the reference dataset, extracted from individual simulation nodes, are compared to the data averaged over each cell of the 7th beam of the V-ADCPs (Figure 9). This beam is oriented vertically upward and matches the position of the vertical reference profile. The vertical evolution of the Reynolds stresses derived from both the reference dataset and the V-ADCPs are similar. However, the V-ADCP data significantly and systematically underestimates the magnitude of the Reynolds stresses, especially for the normal stresses. This result is in agreement with the right-skewed distribution of the scatterplots associated with the normal stresses presented in Figure 5. For each component, the difference is more significant in the lower part of the water column and ranges from 10 % to 20 %.

Conclusion

In this study, the ability of a coupled 4-beam ADCP system to characterise the six components of the Reynolds stress tensor is assessed. LES of high Reynolds flow over a rough bed is performed in order to build a reference synthetic dataset used to directly estimate the Reynolds stresses. The coupled ADCP system (V-ADCP) is assumed to be located on the seabed measuring the along-beam velocities of the synthetic flow [START_REF] Vermeulen | Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows[END_REF]]. The Reynolds stresses derived from the V-ADCPs are estimated following the methodology proposed by [Thiébaut et al. (2020c,b)].

Comparison between Reynolds stresses derived from both the reference dataset and the V-ADCPs are generally in good agreement. The flow heterogeneity over the ADCP beams and the spatial averaging over ADCP cells are found to be the two main sources of error in the interpretation of ADCP measurements.

Flow heterogeneity is observed in the lower part of the water column, where the seabed roughness wakes have a local influence on the turbulence metrics. It is significant up to twice the roughness height (6 m). This leads to high discrepancies between V-ADCP and reference results. As a consequence, ADCP measurements should be interpreted with caution near the seabed in the case of a high seabed roughness.

Flow heterogeneity is also observed in the upper part of the water column, where the distance between beams increases. The heterogeneity is observed in the lateral direction and not in the longitudinal direction. Indeed, the transport of turbulence characteristics in the longitudinal direction is expected to be faster than its diffusion in the lateral direction, resulting in a higher homogeneity in the longitudinal direction than in the lateral direction. However, this heterogeneity is expected to have a minor effect on the accuracy of the measurements, since Reynolds stresses derived from the reference dataset and the V-ADCPs are found to be consistent.

The spatial averaging over the cells in the numerical model is found to underestimate the Reynolds stresses by 10 % to 20 %, in particular the normal components which are used to estimate the turbulence intensity. The spatial averaging is performed to simulate the working principle of a real ADCP. However, for this type of sensor, the averaging is not uniform over the cells. Instead, the cells are most sensitive to velocities at their centre and least sensitive at the edges. The velocity in each depth cell is a weighted average using a triangular weighting function. This is not considered in the present study.

These insights could help reducing uncertainties and systematic bias of in situ measurements and thus improve the knowledge about environmental flows. This improvement would benefit turbine manufacturers in the optimisation of turbine design.

This work is based on a unique simulation configuration characterised by its flow velocity, size and spacing of roughness and water column height. These conditions are representative of flows at typical tidal energy sites, where the general conclusions of this work would apply. Nevertheless, it is expected that different types of flow would potentially lead to different conclusions.

Real seabed morphology is diversified, as well as environmental flow characteristics. The flow obtained in this study from an idealised seabed roughness cannot be assumed to be representative of all environmental flows. Thus, the conclusions of the present work must be put into perspective with the actual seabed and hydrodynamic conditions of any other specific studied site.

V-ADCPs do not take all biases into account. Numerical simulations are an idealised environment that do not include physical processes leading to the acquisition of data outliers. The conclusions proposed here, give insight for quantifying some sources of error but do not exonerate from usual corrections and uncertainties applied in ADCP measurements such as the bias in turbulence measurements induced by the Doppler noise.

For future work, new simulations could be conducted, using different seabed geometries, water depth and averaged velocity magnitudes. This would help in understanding the effect of these parameters on the accuracy of the tested ADCP configuration and provide more insight into the interpretation of real ADCP measurements. V-ADCPs could be implemented with more detailed numerical models to take into account physical phenomena that are neglected in this study (such as spatial averaging over an ADCP cell). This would improve the fidelity of V-ADCP data acquisition with respect to real ADCPs and reinforce the relevance of the conclusions and prescriptions obtained from V-ADCP analysis. Also, the V-ADCP method could be used, not only for turbulence measurements, but also for average velocity measurements. In particular, it could be used to assess the potential improvement brought by ADCPs based on higher acquisition frequencies. Finally, the simulation of realistic environmental flows combined with the V-ADCP method could help testing new ADCP beam configurations. The sensitivity of the measurements to the number of beams, beam orientations, cell thickness or acquisition frequency could be assessed to optimise these parameters for measurements performed in specific environments.

  al. (2010)]. Bottom mounted Acoustic Doppler Current Profilers (ADCPs) are commonly used for flow characterisation in situations where simultaneous velocity measurements are desired throughout the water column, to investigate the vertical distribution of the current velocities. ADCPs use the Doppler shift in the echoes of a pulsed signal along directed acoustic diverging-beams to estimate flow velocities. Such sensors can be deployed in various environments such as oceans, rivers or estuaries and for long intervals of time (several months), allowing for an assessment of the flow variability over a wide range of time scales, with a typical sampling frequency of a few hertz. They can be employed for an extensive range of applications and especially for turbulence characterisation [McMillan et al. (2016); Guerra et al. (2017); Thiébaut et al. (2020a)]. Velocity fluctuations derived from ADCP measurements enable the quantification of several characteristics of the turbulent kinetic energy (TKE) budget such as the TKE dissipation and TKE production rate, as well as the diffusive transport term [Thiébaut et al. (2020c)]. The use of 4-beam ADCPs for turbulence characterisation gained popularity since [Lohrmann et al. (1990)] introduced the so-called variance method. With this technique, profiles with two components (out of six) of the Reynolds stress tensor are estimated from along-beam velocity measurements, using the difference between the velocity variances along opposing beams [Lu and Lueck (1999); Stacey et al. (1999); Rippeth et al. (2003)]. In comparison to 4-beam ADCPs, 5-beam ADCPs allow for a true measurement of vertical velocities and the estimation of five components of the Reynolds stress tensor [Guerra et al. (2017)], and reduce wave disturbances [Togneri et al. (2017a)]. Recently, 7-beam ADCPs have emerged [Droniou et al. (2019)], enabling the full Reynolds stress tensor to be solved but they still require development and validation. A valuable alternative to 7-beam ADCPs, for fully resolving the Reynolds stress tensor, is the combination of two 4-beam ADCPs [Vermeulen et al. (2011)]. The data from the eight beams allow the six components of the tensor to be resolved. Recently, this method has been implemented to coupled ADCP measurements performed in the Goulet de Brest, France [Pieterse et al. (2017)] and in the Raz Blanchard [Thiébaut et al. (2020c,b)].

  al. (2013); Basley et al. (2019)] and numerically by [Coceal et al. (2007); Anderson et al. (2015)]. [Hardy et al. (2016); Jiang and Liu (2018)] also performed experimental and numerical analyses of flows over a pebble bed. [Ikhennicheu et al. (2018, 2019, 2020); Mercier et al.

  ; Qian et al. (1992)], a full description of which can be found in [Guo and Shu (2013)]. The code is based on Palabos, a C++ library [url]. LES relies on the static Smagorinsky model [Smagorinsky (1963)], with a Smagorinsky constant of 0.14. The discretisation scheme is D3Q19, and the collision operator relies on the work of [Latt and Chopard (2006)]. A no-slip boundary condition is used at the seabed, based on the work of [Bouzidi et al. (2001)]. Periodic boundary conditions are applied at the longitudinal and lateral boundaries. A free-slip boundary condition is applied at the water surface position. The simulation domain is 320 m long, 80 m wide and 40 m deep.

Figure 1 :

 1 Figure 1: Domain dimensions and cube arrangement.

Figure 2 :

 2 Figure 2: Isosurfaces of instantaneous longitudinal velocity. LBM simulation of a turbulent flow in conditions representative of the hydrodynamics of the Raz Blanchard. Seabed composed of cubic macro-roughness. Image dimensions: 320 m x 40 m.

(

  radial velocities) at the frequency rate of 2 Hz. The angle θ between the transducers and the vertical is 20˚, in accordance with the 4-beam ADCPs used in [Vermeulen et al. (2011); Thiébaut et al. (2020c,b)]. A Cartesian coordinate system (O, x, y, z)

  is the transformation matrix involving sines and cosines of θ, φ 1 , φ 2 and φ 3 [Vermeulen et al. (2011); Thiébaut et al. (2020c,b)]. The velocities in the Cartesian coordinate system are obtained by inverting the transformation matrix, T . In order to obtain the components of the Reynolds stress tensor from the velocity variances in beam coordinates, a new eight by six matrix, Q, is computed resulting from the product of the terms in T [Vermeulen et al. (2011); Thiébaut et al. (2020c,b)]. The vector v b containing the velocity variances in beam coordinates is written as the product of Q by the vector r containing the six terms of the Reynolds stress tensor, as in Equation

Figure 3 :

 3 Figure 3: Position and orientation of two coupled 4-beam ADCPs [Vermeulen et al. (2011)].

  (a) Side view. (b) Plan view.

Figure 4 :

 4 Figure 4: Visualisation of the eight beams of the V-ADCP configuration. Each alternate grey and red stripe corresponds to an individual cell.

Figure 5 :

 5 Figure 5: Comparison of the Reynolds stresses derived from V-ADCP and reference data. Each dot stands for a different elevation through the water column, between 3.3 m and 31 m, as shown by the colour bar.

(m 2 .s - 2 )Figure 7 :

 227 Figure 7: Vertical profiles of the Reynolds stresses derived from the reference dataset along each beam of the V-ADCP.

  u w , v v , w w (m 2 .s -2 ) m 2 .s -2 )(b) Normalised average difference with the average value.

Figure 8 :(m 2 .s - 2 )Figure 9 :

 8229 Figure 8: Evaluation of the dispersion of Reynolds stresses over the 8 V-ADCP beams.

Table 1 :

 1 Max and root mean square relative errors between reference and V-ADCP data for all components of the Reynolds stress tensor above 8 m elevation.

	Max relative error (%) 20 RMSE (%) 8	27 14	22 12	91 33	34 11	353 137

Acknowledgments

This work benefits from a French State grant managed by the National Research Agency under the Investments for the Future program bearing the reference ANR-10-IEED-0006-11 and is also funded by the INTERREG TIGER project. The authors acknowledge the financial support of CD50 and Région Normandie. We are grateful to the CRIANN ("Centre Régional Informatique et d'Applications Numériques de Normandie") for providing computational means.


Thomas Thiebault

Laetitia Fougère

Anaëlle Simonneau

Emilie Destandau

Claude Le Milbeau

Jérémy Jacob

Occurrence of human-excreted contaminants within a decantation tank: A clue of their historical consumption?

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Occurrence of human-excreted contaminants within a decantation tank: a clue of historical consumption? T. Thiebault 1 , L. Fougère 2 , A. Simonneau 3 , E. Destandau 2 , C. Le Milbeau 3 , J. Jacob 4 1 METIS, UMR 7619, SU, CNRS, EPHE, Paris, France 2 ICOA, UMR 7311, Univ. Orléans, CNRS, Orléans, France 3 ISTO, UMR 7327, Univ. Orléans, CNRS, BRGM, Orléans, France 4 LSCE, UMR 8212, CEA, UVSQ, CNRS, IPSL, Gif-sur-Yvette, France

The Earth system is enduring a unique transition in its history due to the pregnancy of human activities on geological processes compared to natural controls. A large community examines the extent to which these activities will be archived in the sedimentary record and remain for millions years within a new geological era named Anthropocene. Here we explore the potential of sediments that accumulated in sewer systems for such a record of human posterity, considering that urban socio-ecosystems are prone to a large diversity and high concentrations of potential tracers of human activities [START_REF] Zalasiewicz | When did the Anthropocene begin? A mid-twentieth century boundary level is stratigraphically optimal[END_REF].

The selected site is a decantation tank that collects wastewater and stormwater from the sewer network of the northern part of Orléans (France). This 20 m deep underground building of cylindrical and conical shape was constructed in 1942 and was reputed to have not been subjected to any clean out operation (COO) since that time. 5 cores (i.e. 8m of sediments) were acquired from 2014 to 2017 by manually inserting a plastic tube in the outcropping sediments or with a gravity corer prior to COO. 152 samples were taken and investigated in this work. These samples were extracted with a mixture of water:methanol (1:1) in order to obtain drugs and illicit drugs that were then quantified by HPLC-MS². Extracted sediments then underwent a large range of classical sedimentological analyses (e.g. granulometry, facies description). Total organic carbon, Hydrogen Index, Oxygen Index and Tmax were determined by Rock-Eval pyrolysis. The age model is based on 47 14 C dates obtained on the 6 cores and computed with OxCal v4.3.2 and Bomb13NH1 calibration curve.

Oldest sediments are dated back to 1970. This reveals that COO certainly took place at the end of the seventies, with no administrative or written record subsisting. Sedimentation rates are then very high with 6 m deposited in two years, which corresponds to accumulation rates observed after the 2015 COO. Then, sedimentation rates slowed down with only 2.5 m accumulated from 1980 to 2014 because the decantation tank was saturated and could not accumulate more sediments. Hence, repeated episodes of erosion compensated by deposition are suspected over that period. Sediments are stratigraphically organised into organic (TOC > 2%) and mineral (TOC < 2%) layers resulting from wastewater and stormwater inputs, respectively.

Among the 27 investigated drugs and illicit drugs, some compounds such as ciprofloxacin, ofloxacin or tetrahydrocannabinol could not be detected in the sediments. For the other detected compounds, a strong control of speciation on the presence and concentration of drugs and illicit drugs is evidenced [START_REF] Rivett | Increase organic contaminant residence times in the urban riverbed due to the presence of highly sorbing sediments of the Anthropocene[END_REF].

Neutral and anionic compounds (e.g. carbamazepine, salicylic acid) present higher occurrences in the organic facies whereas cationic compounds (e.g. codeine, benzoylecgonine) display more regular occurrences, whatever the facies. The distribution of non-cationic molecules is therefore directly correlated with the distribution of organic carbon, whereas for the cationic ones, a correlation with the relative abundance of inorganic surfaces is evidenced. As a result, the interaction mechanisms between targeted compounds and the sedimentary composition appears to be the most important control of their occurrences (Figure 1). Finally, for some compounds such as cocaine and MDMA, the concentration decreases with the depth, indicating a potential degradation pattern. This type of pattern is for example emphasized by the relative increase of the benzoylecgonine/cocaine ratio with depth (i.e. benzoylecgonine is one of the main metabolite of cocaine, less sensible to degradation). The analysed sediments present important vertical variations of composition, due to distinct origin (i.e. wastewater/stormwater), especially emphasized by the organic carbon variations. Hence, drugs and illicit drugs distributions appear to be strongly controlled by their theoretical affinity with solids. As a result, the distribution of these compounds with time cannot be directly correlated with the evolution of excretion amount in the catchment, as initially expected. Nevertheless, these patterns are very informative on the affinity between sediments and organic contaminants at a larger scale.

Figure 1

 1 Figure 1 Schematic representation of the origin and possible reactivity of solids samples in the decantation tank.