domain: spi phys

text:
Huret Thomas
email: thomas.huret@onera.fr

Tanguy Geoffrey

Vassilicos Christos

Jacquin Laurent

Gallas Quentin

Design of multiscale inhomogeneous grids for the generation of atmospheric boundary layer logarithmic mean flows

Wind tunnel generation of flows representative of the Atmospheric Boundary Layer (ABL) still requires trial-and-error based design processes for both passive and active devices. To address this issue, a new type of passive grids -Multiscale Inhomogeneous Grids (MIGs) -is presented. It takes advantage of obstruction variations and interacting wakes to tailor both mean flow profile and turbulent intensity profiles downstream the grid. The present work derives theoretical models in order to predict the mean velocity profile of MIG-generated flows characteristics for applications to neutral atmospheric boundary layer. These prediction models are investigated experimentally downstream of MIGs using Hot-Wire Anemometry within the SCL-PIV subsonic wind tunnel at ONERA Lille (Section ܪ × ܹ = 290݉݉ × 300݉݉, velocities up to 30 .)ݏ/݉ First, the mean velocity profile prediction, based on McCarthy (1954), is applied with MIGs to generate logarithmic mean profiles for an equivalent roughness length ℎ consistent with the characterized roughness of LEGO® baseboard surface. The interaction of these grid-generated flows with artificial roughness is then investigated, showing a good fit in the central region, yet revealing clear discrepancies in the wall-affected region, contrary to past boundary layer generating devices, such as spires. The study concludes on the need for further understanding of the turbulence characteristics of the generated flows, also mandatory for the current development of a turbulence prediction model.

Introduction 1.1 The Atmospheric Boundary Layer (ABL) in wind tunnel

The experimental generation of wind tunnel flows representative of the Atmospheric Boundary Layer (ABL) has been investigated during the last decade of the 20 th century with both passive [START_REF] Counihan | An improved method of simulating an atmospheric boundary layer in a wind tunnel[END_REF][START_REF] Hunt | Wind-tunnel simulation of the atmospheric boundary layer: a report on Euromech 50[END_REF][START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF][START_REF] Irwin | The design of spires for wind simulation[END_REF] and active devices [START_REF] Hearst | Tailoring incoming shear and turbulence profiles for lab-scale wind turbines[END_REF]. Similarity criteria were derived by [START_REF] Cermak | Laboratory Simulation of the Atmospheric Boundary Layer[END_REF] [START_REF] Cermak | Laboratory Simulation of the Atmospheric Boundary Layer[END_REF] and [START_REF] Avissar | Operating ranges of mesoscale numerical models and meteorological wind tunnels for the simulation of sea and land breezes[END_REF] [START_REF] Avissar | Operating ranges of mesoscale numerical models and meteorological wind tunnels for the simulation of sea and land breezes[END_REF] who emphasized the impossibility of reaching a configuration fully similar to the atmospheric case. Attempts of reproducing the ABL in wind tunnels are therefore focused on the reproduction of the main flow characteristics. [START_REF] Armitt | The simulation of the atmospheric boundary layer in a wind tunnel[END_REF] [START_REF] Armitt | The simulation of the atmospheric boundary layer in a wind tunnel[END_REF] reviewed the wind engineering requirements depending of the application (e.g. civil engineering or pollutant dispersal) and listed the flow characteristics of interest to be mainly the vertical profiles of mean velocity, turbulence intensity components and turbulence integral length scales.

The roughness similarity criteria by [START_REF] Jensen | Model-scale tests in turbulent wind[END_REF] [START_REF] Jensen | Model-scale tests in turbulent wind[END_REF] is of significant importance for the reproduction of these flow quantities, especially close to the wall. It states that the Jensen number ݁ܬ = ℎ ܦ/ should be conserved between the wind tunnel and the represented atmospheric configuration, where ℎ stands for the "roughness length" and ܦ represents either the boundary layer depth (if fully reproduced in wind tunnel) or the wind tunnel full height (if only part of the boundary layer is reproduced within the full wind tunnel section). The wind tunnel configurations studied in this work are representative of neutral ABL over flat surfaces of homogeneous roughness, quantified by the "roughness length" ℎ . This quantity is defined through the mean velocity profile obtained in the Inertial SubLayer (ISL) of the ABL, characterized by a logarithmic dependency with the altitude [START_REF] Monin | Basic laws of turbulent mixing in the surface layer of the atmosphere[END_REF] (see Figure 1), as described by the equation:

ݑሺݖሻ = ݑ * ߢ ln ൬ ݖ െ ݀ ℎ ൰ ሺ1ሻ
The friction velocity ݑ * is defined as ݑ * : = ఛ →ೢೌ ఘ ൎ ඥെ〈〉′ݓ′ݑ ௪ . This behaviour is analogous to the log-law observable within classic rough-wall turbulent boundary layer, since the ABL is equivalent to such flow in case of negligible vertical heat flux (neutral ABL) [START_REF] Raupach | Rough-Wall Turbulent Boundary Layers[END_REF].

At high Reynolds number, the roughness length is a function of the roughness elements geometry only [START_REF] Raupach | Rough-Wall Turbulent Boundary Layers[END_REF]. Classifications were suggested [START_REF] Davenport | The application of a the boundary layer wind tunnel to the prediction of wind loading[END_REF][START_REF] Counihan | Further measurements in a simulated atmospheric boundary layer[END_REF] to relate a class of terrain to a roughness length, leading to a range of ℎ between 0.0003 ݉ and 2 ݉ for the revised Davenport's classification (2000).

Davenport & Isyumov (1967) [START_REF] Davenport | The application of a the boundary layer wind tunnel to the prediction of wind loading[END_REF] showed that the best available device to reproduce a full ABL is the natural growth of a turbulent boundary layer over a roughness fetch long of about 25 to 35 the depth of the desired boundary layer. Such high aspect ratio is in general out of reach for most of the aerodynamic wind tunnels in use, therefore, the next devices were attempting to reduce this development length by artificially thickening the boundary layer. In particular, the Counihan-type configurations [START_REF] Counihan | An improved method of simulating an atmospheric boundary layer in a wind tunnel[END_REF][START_REF] Zheng | Weakly sheared turbulent flows generated by multiscale inhomogeneous grids[END_REF] were successful in reproducing the atmospheric mean flow profile and correct profiles of turbulence intensities. Inspired by this device, [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF] [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF] presented a family of configurations and suggested a general understanding of the behaviour of such devices, named as "roughness-barrier-mixing device method" (RBM). This was observed by [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF] [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF] who undertook a parametric analysis on their devices to relate the effective roughness length and integral length scales to their geometric parameter (the height of the wall component, see Figure (2c)).

Irwin (1981) [START_REF] Irwin | The design of spires for wind simulation[END_REF] summarized a successful attempt to tailor the mean flow profile (not the turbulent intensity profile) using a simple geometry ("spires" and roughness) related to the downstream mean flow characteristics by empirical and theoretical models [START_REF] Irwin | Design and use of spires for natural wind simulation[END_REF]. These technics are widely used by both research and industrial communities, even though it cannot tailor turbulence intensity independently of mean flow profile.

Objectives

The present work aims at reproducing experimentally a logarithmic mean flow by associating roughness and a recently introduced passive grid device. Such configuration is thought to be representative of the atmospheric Surface Layer (see Figure 1). Multiscale Inhomogeneous Grids are passive devices introduced recently by Zheng et al (2018) [START_REF] Zheng | Weakly sheared turbulent flows generated by multiscale inhomogeneous grids[END_REF]. Their design is expected to enable tailoring (without trial-and-error) both mean flow profile and turbulent intensity profiles, by taking advantage of tools developed initially for fractal grids studies.

The next section presents the past work establishing ways to design a grid for a given mean flow profile.

Multiscale Inhomogeneous Grids (MIGs) design 2.1 Multiscale Inhomogeneous Grids

Multiscale Inhomogeneous Grids [START_REF] Zheng | Weakly sheared turbulent flows generated by multiscale inhomogeneous grids[END_REF] are composed of regular arrays of vertical bars within several horizontal levels of varying geometric properties ݓ( , ݃ , ℎ , see Figure 3). Assuming that the lateral walls of the wind tunnel act as mirrors for the flow, the choice ݎ = మ theoretically minimizes the boundary effects that could occur, by mimicking an infinitely periodic set of vertical bars. Each level is finally characterized by its local blockage ratio (i.e. ratio between the filled area and the total area of the level), computed as:

ߪ = ⎩ ⎪ ⎨ ⎪ ⎧ ܿ ݓ ሺℎ െ ܶ ሻ ܶ ܹ ℎ ܹ for n ∈ ሾ|1, ܰ െ 2|ሿ ܿ ݓ ሺℎ െ ܶ ሻ ଵ ଶ ܶ ܹ ൫ℎ െ ଵ ଶ ܶ ൯ܹ for ݊ = 0 or ݊ = ܰ െ 1

Theoretical prediction of the mean flow profile

The MIGs are composed of multiple horizontal layers, each of them harbouring an array of vertical bars of the same width. Width and distance between two vertical bars are dependent of the grid level. The non-uniform local blockage ratio that is produced generates a non-uniform pressure jump between the two sides of the grid. This pressure jump, normalized as ܭ = ሺܲ ି െ ܲ ା ሻ/½ρݑ ଶ in the following, produces a non-uniform pressure field upstream and downstream, both of which influencing the mean flow velocity. The grid geometry is therefore a way to convert the far upstream mean flow distribution ݑ ିஶ into a sheared mean flow far downstream ݑ ାஶ (see Figure 3). The influence of the blockage ratio of a uniform gauze on the flow features has been studied first by [START_REF] Taylor | THE EFFECT OF WIRE GAUZE ON SMALL DISTURBANCES IN A UNIFORM STREAM[END_REF] [START_REF] Taylor | THE EFFECT OF WIRE GAUZE ON SMALL DISTURBANCES IN A UNIFORM STREAM[END_REF]. [START_REF] Owen | The production of uniform shear flow in a wind tunnel[END_REF] [START_REF] Owen | The production of uniform shear flow in a wind tunnel[END_REF] explored the possibilities of producing a uniform shear flow using a non-uniform local blockage ratio distribution. The theoretical reasoning was further developed by [START_REF] Elder | Steady flow through non-uniform gauzes of arbitrary shape[END_REF] [START_REF] Elder | Steady flow through non-uniform gauzes of arbitrary shape[END_REF] and then by [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF] [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF], reaching an equivalent formulation of the same equation model (see Equation ( 2)), but studied with two different sets of assumptions. As summarized in [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF] [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF], the reasoning is derived with the assumptions that: (i) the grid is a fluid interface out of which viscosity effects are negligible, (ii) the Reynolds stresses are neglected in the Reynolds-Averaged Navier Stokes (RANS) equation, (iii) the deflection of streamlines is negligible (i.e. ݒ ≪ ݑ and ݓ ≪ )ݑ and (iv) the resulting mean flow has no swirling components.

൮൦ ܤ ߯ ଶ ߯ ଶ െ 1 ቀ1 ܤ ߯ ቁ ଶ ߯ 1 ܤ ߯ ൪ ൬ݑ ାஶ ܤ ߯ ݑ ିஶ ൰ െ ܤ ߯ ଶ ߯ ଶ െ 1 1 ܤ ߯ ݑ ିஶ ൲ ݀߯ ൮1 ߯ ଶ െ 1 1 ܤ ߯ ൲ ݑ݀ ାஶ ൮ ܤ ߯ ሺ߯ ଶ െ 1ሻ 1 ܤ ߯ െ 1൲ ݑ݀ ିஶ = 0 ሺ2ሻ
Where: ߯ = √1 ܭ is associated to the grid-generated pressure jump distribution and 1.1~ܤ is a constant empirically deduced by [START_REF] Taylor | THE EFFECT OF WIRE GAUZE ON SMALL DISTURBANCES IN A UNIFORM STREAM[END_REF] [START_REF] Taylor | THE EFFECT OF WIRE GAUZE ON SMALL DISTURBANCES IN A UNIFORM STREAM[END_REF] in order to relate the pressure jump ܭ and the deflection coefficient ߙ by the expression ߙ = 1√/ܤ .ܭ There is no clear consensus on the relation between ܭ and the grid geometry, even though several empirical laws were suggested to relate it to the grid local blockage ratio (see for instance Karnik & Tavoularis 1987 [START_REF] Karnik | Generation and manipulation of uniform shear with the use of screens[END_REF]). [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF] [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF] considered the Equation (3) coming from [START_REF] Wieghardt | On the Resistance of Screens[END_REF] [START_REF] Wieghardt | On the Resistance of Screens[END_REF], with a coefficient ݎ depending on the interstitial Reynolds number ܴ݁ = ݑ /ݓሺሺ1 െ ߪሻߥሻ with ݓ the width of the considered grid bar.

ܭ = ߪݎ ሺ1 െ ߪሻ ଶ ሺ3ሻ
McCarthy (1964) [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF] considered the value of ݎ = 0.78 while Zheng et al (2018) [START_REF] Counihan | Further measurements in a simulated atmospheric boundary layer[END_REF] preferred ݎ = 0.7, observed by [START_REF] Cornell | Losses of flow normal to plane screens[END_REF] [START_REF] Cornell | Losses of flow normal to plane screens[END_REF] up to ܴ݁ = 4 × 10 ସ (typical values in our cases lie between 10 ଷ and 10 ସ ). Another formulation is given by Roach (1987) [START_REF] Roach | The generation of nearly isotropic turbulence by means of grids[END_REF] in Equation ( 4).

ܭ = ܣ ൬ 1 ሺ1 െ ߪሻ ଶ െ 1൰ ሺ4ሻ
The parameters ܣ and ܤ depends on the Reynolds number and the grid bars/mesh geometry. [START_REF] Roach | The generation of nearly isotropic turbulence by means of grids[END_REF] [START_REF] Roach | The generation of nearly isotropic turbulence by means of grids[END_REF] estimated them experimentally for different grids configuration by changing both the mesh (parallel bars or square mesh) and the grid bars geometry (square or circular sections). It appears that the two coefficients mainly depend on the section of the bars as summarized in the Table [START_REF] Hunt | Wind-tunnel simulation of the atmospheric boundary layer: a report on Euromech 50[END_REF].

Table 2 : Empirical estimation of coefficients for Equation (4) from [START_REF] Roach | The generation of nearly isotropic turbulence by means of grids[END_REF] [START_REF] Roach | The generation of nearly isotropic turbulence by means of grids[END_REF] Circular

McCarthy (1964) model

McCarthy (1964) [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF] considered the far upstream flow to be perfectly homogeneous ݑ݀( ିஶ = 0 and ݑ ିஶ = ݑ ሻ so that the Equation ( 2) becomes a non-linear Ordinary Differential Equation on ݑ ାஶ as a function of ߯. This equation was solved analytically by approximating several integrals up to the second order (see [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF]). The resulting relation between normalized mean flow profile and normalized pressure jump is given in Equation ( 3) for a problem discretized over the N levels of the designed grid.

݂ ା = 1 െ 1,01ࣛሺܭ ሻሺℬሺܭ ሻ െ ߛ ሻ ሺ5ሻ With ࣛሺܭ ሻ = ଵାඥଵା ൫ଵାሺଵା ሻ య/మ ൯ మ/య ℬሺܭ ሻ = భ ల ାሺଵା ሻ య/మ ଵା ߛሺሼܭ ሽ ሻ = ∑ ࣛሺ ሻℬሺ ሻ ಿషభ సబ ∑ ࣛሺ ሻ ಿషభ సబ
This non-linear coupled equation system is inverted by a Sequential Least Squares Programming (SLSQP) algorithm in order to find the ሼܭ ሽ distribution that would minimize the cost function ܨሺሼܭ ሽ ሻ = ∑ ሺ݂ ା െ ேିଵ ୀ ሾ1 െ 1,01ࣛሺܭ ሻሺℬሺܭ ሻ െ ߛ ሻሿሻ ଶ for a given objective function ݂ ା .

A numerical solving model

Another way to solve Equation ( 2) without asking for extra hypothesis on the upstream mean flow (or analytical approximations) consists in solving it numerically. For prescribed normalized upstream and downstream mean flow, Equation ( 2) can be rewritten as:

߲߯ ݖ߲ = ܩ ା ሺ߯ሻ ݂݀ ା ݖ݀ ܩ ି ሺ߯ሻ ݂݀ ି ݖ݀ ቂℳሺ߯ሻ െ ܤ ߯ ቃ ݂ ି െ ℒሺ߯ሻ݂ ା ܽ݊݀ ߯ሺݖ = 0ሻ = ߯ ሺ6ሻ With ܩ ା ሺ߯ሻ = 1 ఞ మ ିଵ ଵା ಳ ഖ , ܩ ି ሺ߯ሻ = ಳ ഖ ൫ఞ మ ିଵ൯ ଵା ಳ ഖ െ 1 ℳሺ߯ሻ = ఞ మ ఞ మ ିଵ ଵା ಳ ഖ , ℒሺ߯ሻ = ఞ మ ఞ మ ିଵ ቀଵା ಳ ഖ ቁ మ ఞ ଵା ಳ ഖ ൩
The solution of this problem, numerically computed using a Runke-Kutta 4 (RK4) method, is then discretized over ܰ grid levels. The final problem consists in finding the correct initial condition in order to obtain the prescribed mean blockage ratio expected over the full section. This is realized by a dichotomy algorithm.

Grid design algorithm

Using the mean flow tailoring tools described above, a grid design algorithm was implemented in two versions depending of the modelling choice. They can be visualized schematically in Figure [START_REF] Hearst | Tailoring incoming shear and turbulence profiles for lab-scale wind turbines[END_REF] and Figure [START_REF] Cermak | Laboratory Simulation of the Atmospheric Boundary Layer[END_REF]. Choice was made to arbitrarily fix the distance ݃ between two adjacent bars and the height of each grid level, since they represent extra-degrees of freedom that will become useful only for generating prescribed turbulence profiles. The wind tunnel has the specificity to enable the easy insertion of grids through 15 mm-wide and 5 mm depth slots (see Figure [START_REF] Avissar | Operating ranges of mesoscale numerical models and meteorological wind tunnels for the simulation of sea and land breezes[END_REF] and Figure ( 8)). Upstream of this location, an empty section is dedicated to produce a homogeneous parallel flow after a 200 mm long and 10 mm high bevel. The empty vein characterization reveals boundary layers at the grid location of 10 mm high (results not shown). Figure [START_REF] Kaimal | Atmospheric Boundary Layer Flows: Their Structure and Measurement[END_REF] is consistent with the expected ℎ ௦௧ = 0.0025 ݉݉ [START_REF] Raupach | Rough-Wall Turbulent Boundary Layers[END_REF] and ℎ ாீை = 0.13 mm [START_REF] Counihan | An improved method of simulating an atmospheric boundary layer in a wind tunnel[END_REF]. Therefore, it is this value that has been chosen as an input for the logarithmic objective function that will be generated for the next sections.

Definition of the 6 grids

In the present work, six different grids were designed in order to fit within the SCL-PIV slot. A 3-side frame is added to the grid for insertion in SCL-PIV wind tunnel. It is designed in order to be flush with the wind tunnel walls. All of the grids (except the spires configuration) share the same characteristics for their horizontal bars (a width ܶ = 1.66 ݉݉ and a depth ݀ = 10 ݉݉). The different grids are listed in Figure [START_REF] Raupach | Rough-Wall Turbulent Boundary Layers[END_REF].

The five first grids/obstacles are designed in order to generate the same objective mean flow: a logarithmic mean flow with artificial roughness ℎ ௧௩ ܪ/ = 4.5 × 10 ିସ (compatible with LEGO® Baseboard roughness, see Figure [START_REF] Kaimal | Atmospheric Boundary Layer Flows: Their Structure and Measurement[END_REF])

over the full section of the wind tunnel. The Figure [START_REF] Davenport | Estimating the roughness of cities and sheltered country[END_REF] reveals that roughness has a very low influence above the equivalent boundary layer height growing in no-grid condition. Indeed, the log-law parameters obtained in the center region of the wind tunnel section remain similar to their values without roughness. However, closer to the wall, the roughness does not seem to correct properly the ℎ discrepancy with the design input observed at these altitudes without roughness. Far from having a correction effect, supposedly leading to identical parameters between center region and wall-region, the roughness seems to have a too high decelerating effect. In wall-region, our grid-roughness data are not sufficiently close to the wall to be fully conclusive on the log-law parameters within region. Therefore, new measurements are currently undertaken to better characterize this region. This new database will help quantify the exact influence of the roughness, so that it will be possible to take it into account in the grid design.

Nevertheless, the conclusion is significantly different for "MIG-spires-log-LEGO_N15" (Figure ( 14) -d) where the two flow regions effectively show the same logarithmic parameters. This success is consistent with previous successful passive devices, such as the Irwin (1981) [START_REF] Irwin | The design of spires for wind simulation[END_REF] spires-roughness combination. It shows that spires generated using the McCarthy model give satisfactory results in the same way as these previous methods. On the contrary, grids interact in a different way with roughness, probably because of their specific turbulent structure scales and density, which depends on the scales of the grid mesh.

Turbulence intensity

The streamwise turbulence intensity measured at the location "IIIT9-Center" (see Section 3.1) corresponding to "MIGnh-rk4-log-LEGO_N15" (d) and "MIG-spires-log-LEGO_N500" (e) are presented in Figure [START_REF] Davenport | The application of a the boundary layer wind tunnel to the prediction of wind loading[END_REF]. Conclusions with the other grids are similar to the one with "MIG-nh-rk4-log-LEGO_N15". As it was the case for mean flow profiles, the wind tunnel center region (roughly between 0.2H and 0.8H) is very weakly affected by the roughness change. For all the cases, the center-region turbulence is too weak compared to the atmospheric requirements. However, spires appear to produce significant turbulence intensity up to high altitudes. On the contrary, the grid generated flow only shows high turbulence in the wall-affected region, and low intensity (up to 2%) in the grid-affected region. This is consistent with the well-known observation that passive grid-generated turbulence decay faster [START_REF] Hunt | Wind-tunnel simulation of the atmospheric boundary layer: a report on Euromech 50[END_REF][START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF], due to smaller turbulence production length scales.

Conclusion & perspectives

This work shows the first investigations undertaken to explore the possibilities of generating a prescribed mean flow representative of atmospheric boundary layer with Multiscale Inhomogeneous Grids (MIGs). The choice of this type of grids is justified by its capacity to tailor turbulence intensity. Before reaching this turbulence control step, the present work is mainly interested in validating the mean flow tailoring by MIGs. Two models are suggested, both depending on the theoretical reasoning explicited by [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF]. With 6 different grids or obstacles designed using these models, the center vein is shown to depend mainly on the grid characteristics, showing a good match with the expected mean velocity profiles.

However, the wall-region remain mainly influenced by the wall roughness. Surprisingly, an attempt to reach roughness similarity led to larger discrepancies, except for the "spires" configuration, which shows a very good match with the expected mean flow even within the wall region. This reveals that the geometric differences between grid and spires have a significant influence on the interaction with roughness. This is probably due to the larger vortex structures produced by spires, which enable a coupling of flow layers over a significant range of altitudes (as explained by [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF] [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF]). Downstream of passive grids, turbulent structures scale with the mesh size (e.g. [START_REF] Valente | The decay of turbulence generated by a class of multiscale grids[END_REF][START_REF] Nedić | Energy dissipation scaling in uniformly sheared turbulence[END_REF]) and are probably too small to produce the same effect as spires.

This observation motivates the development of prediction model for the integral length scale downstream of MIGs, in order to control more precisely the structures size. This work is currently in progress. Moreover, observation of the turbulent structures past MIGs will be made possible using a stereo-PIV setup. The turbulence intensity prediction model currently in development will benefit from both these integral length scales prediction and these turbulent structures observations.

Figure 1 :

 1 Figure 1: Schematic visualization of the neutral Atmospheric Boundary Layer. Based on [10][11].

Figure 2 :

 2 Figure 2: Several passive devices for the generation of a neutral ABL in wind tunnel However, such devices are designed by trial-and-error for a given atmospheric flow of interest (i.e. for a given roughness). Such trial-and-error process must be reproduced for each new studied configuration and each new wind tunnel setup.

ܹ

  Width of the grid section ܪ Height of the grid section ܶ Width of the horizontal bars ݀ Streamwise depth of the horizontal bars ℎ Height of each layer (horizontal Bars center to center) ݃ Distance between adjacent vertical bars (center to center) ݎ Distance from the wall of the first vertical bar of the level ݓ Width of vertical bars ݀ Streamwise depth of vertical bars ܿ Number of vertical bars ߪ Blockage ratio (solidity) of the layer

Figure 3 :

 3 Figure 3: Several passive devices for the generation of a neutral ABL in wind tunnel

Figure 4 :

 4 Figure 4: Schematic visualization of the regions of influence of the grid upstream and downstream within the wind tunnel.Inspired from[START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF]

a

  Valid for ܴ݁ ௪ = ݑ ିஶ ߥ/ݓ ∈ ሾ10 ଶ , 10 ହ ሿ. More precisely, in this range: ܣ = 0.52 66/ܴ݁ ௪ ସ/ଷ . Typical range for the present work is ܴ݁ ௪ ∈ ሾ10 ଷ , 10 ସ ሿ.b Valid for ܴ݁ ௪ = ݑ ିஶ ߥ/ݓ ∈ ሾ10 ଶ , 10 ସ ሿ. Negligible dependency with ܴ݁ ௪ in this range.Typical range for the present work is ܴ݁ ௪ ∈ ሾ10 ଷ , 10 ସ ሿ.It can be shown from the results by[START_REF] Roach | The generation of nearly isotropic turbulence by means of grids[END_REF] that the Equation (3) is more relevant for the study of grids with circular bars, since Equation (3) and (4) are giving similar values. On the contrary, square bars case gives a relation different by a factor around 2. The next experimental results demonstrate that the Equation (4) with "square bars" parameters gives correct prediction of the MIG-generated mean flows, contrary to circular bars parameters or Equation (3). Therefore, the Equation (4) with square bars case is implicitly kept in the following analysis.

Figure 5 :

 5 Figure 5: Schematic representation of the grid design algorithm using the McCarthy (1964) [19] model.

Figure 6 :3. Experimental setup 3 . 1

 631 Figure 6: Schematic representation of the grid design algorithm solving Equation (2) numerically.The design for grids dedicated to the generation of a logarithmic mean flow is fully characterized by two inputs parameters: the mean blockage ratio ߪ (averaged over the full wind tunnel section area) and the non-dimensional roughness ratio ℎ .ܪ/3. Experimental setup

Figure 7 :

 7 Figure 7: The SCL-PIV wind tunnel (ONERA Lille).

Figure 8 :

 8 Figure 8: Hot-Wire setup inserted through a transverse slot of a removable wood panel. Two different Hot-Wire probes are considered (see Figure (8)). A single Hot-Wire probe with frequency response up to very high frequencies for spectral studies. It also enables to reach points close to the wall. These measurements are complemented by a X-cross Hot-Wires probe leading to two velocity components and Reynolds stress measurements. For every acquisition point of the present work, a signal of 30s is acquired at ݂ = 100 .ݖܪ݇ An analog low-pass filter at ݂ ௨௧ = 30 ݖܪ݇ is applied before acquisition.Three windows enable the exploration of the flow through a total streamwise distance of 1950 mm from the grid insertion slots. These windows are occupied by adaptable wood panels with slots of different orientations depending of the required profile. The current work presents results measured across the "IIIT9-center" profile (wall_normal profile) visible in red in Figure[START_REF] Jensen | Model-scale tests in turbulent wind[END_REF].

Figure 9 : 3 . 2 Figure 10 :

 93210 Figure 9: Schematic visualization of the wind tunnel working section. The "IIIT9-center" profile is highlighted in red

Figure 11 :

 11 Figure 11: Measured mean streamwise velocity profile for the smooth and the rough configurations. The lowest 0.2ߜ ଽଽ -region is fitted using logarithmic law (red lines). The 95% confidence intervals on ℎ ܪ/ estimates are plotted on the Y-axis.

Figure 13 :

 13 Figure 13: Mean longitudinal mean flow velocity profile measured at position ݔ = 1950 ݉ downstream of the grid/obstacles in smooth configuration.

4. 2 Figure 14 :

 214 Figure 14: Mean longitudinal mean flow velocity profile measured at position ݔ = 1950 ݉ downstream of the grid/obstacles in smooth and rough configurations.

Figure 15 :

 15 Figure 15: Streamwise turbulent intensity measured by HWA in SCL-PIV at the location of the "IIIT9-Center" profile. The profiles are compared to the ESDU85020 atmospheric model [27] adapted with the LEGO® Baseboard roughness length.

MIG-log-LEGO_N9

9 levels of same height. Designed with the McCarthy model (1964) [START_REF] Mccarthy | Steady flow past non-uniform wire grids[END_REF].

Experimental investigations 4.1 Grid-alone configurations (no roughness)

The measurements by X-cross hot-wire at the "IIIT9-Center" profile (see Section 3.1) downstream of each grid is presented in Figure [START_REF] Wieringa | Updating the Davenport roughness classification[END_REF]. For each plot, two different regions are visible: a wall-region of approximately the same height as the natural boundary layer growing in empty vein configuration, and a center vein region (roughly between 0.2H and 0.8H) showing a logarithmic evolution of the mean flow profile. Inspired by the flow past a change of roughness, where an inner boundary layer forms within a deeper one, the wall-affected region visible in our results is interpreted as a boundary layer naturally growing within the grid-generated flow. It is of interest to notice that the wallaffected region seems to coincide with the empty vein natural boundary layer (without grid or obstacle).

The profiles within these two regions are fitted by logarithmic laws in order to estimate their equivalent friction velocities and roughness lengths. Such estimation by interpolation of mean profile is known to suffer from large uncertainties [START_REF] Cook | Wind-tunnel simulation of the adiabatic atmospheric boundary layer by roughness, barrier and mixingdevice methods[END_REF], in particular for roughness measurement (due to the exponential relation between roughness length and velocity and the difficulty to access the vicinity of the wall). The 95%-confidence intervals for the estimation of the roughness length are presented as continuous vertical lines on the plots of Figure [START_REF] Wieringa | Updating the Davenport roughness classification[END_REF].

As expected, the wall-region of the profiles always reach the same very low roughness length of the smooth configuration. This observation justifies the need for a roughness similarity of the wall surface with the required value of ℎ , as expressed by the Jensen similarity criterium [START_REF] Jensen | Model-scale tests in turbulent wind[END_REF]. On the contrary, the center of the vein reveals the presence of log-laws (as expected by design) with artificial ℎ ܪ/ of the correct order of magnitude compared to the grid design input. Exceptions to this observation are: (a) "MIG-log-LEGO_N9" and (c) "MIGnh-log-LEGO_N15", which shows values of artificial ℎ respectively too high and too small. These discrepancies could be explain by three reasons: (i) the 3D printing geometric uncertainties; (ii) possible imperfections of the McCarthy model; (iii) the absence of roughness similarity.

By propagating the geometric uncertainty of the 3D-printing process (~0.4 ݉݉ on each geometric parameter) through Equation ( 2), the maximum error on the generated velocity is estimated to be less than 2% in the center region. The hypothesis (i) is therefore considered to be insufficient to fully explain the observed discrepancies. An important observation to investigate the possibility (ii) is the comparison of the grid "MIGnh-log-LEGO_N15" (c) with the grid "MIGnh-rk4-log-LEGO_N15" (d) since the two share the same levels distribution but a different design model. It appears that "MIGnh-rk4-log-LEGO_N15" gives a roughness significantly closer to the design input than "MIGnhlog-LEGO_N15". This observation suggests that the numerical solving of Equation ( 2) represents an improvement


Jean-Baptiste Clément

Damien Sous

Assessment of a wave-forced Richards' equation-based model regarding beach groundwater flow experiments

A numerical model is proposed to analyse the effect of waves in near-shore waters on the beach groundwater flow. The groundwater flow is modelled by Richards' equation which describes flows in variably-saturated porous media. A wave-driven boundary conditions is prescribed at the beach face. The model abilities are assessed against the results of a large-scale laboratory experiment called BARDEX II. This is a sand barrier with a lagoon whose level is controlled. The investigation of water flow rates through the barrier highlights the beach groundwater dynamics under different conditions.

Introduction

Around one-third of the world's ice-free coastline are sandy beaches. Satellite data analysis indicates that a quarter of them are under erosion. There is a serious concern about their future evolution.

Beach groundwater dynamics has become a topic of interest over the years because it controls many processes like biogeochemical cycles, sediment transport, contaminant exchanges, etc. The beach groundwater is mainly governed by the cross-beach gradients induced by tides or large-scale fluctuations of mean water level such as swell and infragravity waves [1]. The swash zone is the beach part subject to waves action. The interaction of the sheet of water with the porous beach causes infiltrations/exfiltrations through the beach face. They can in turn affect the beach groundwater dynamics, especially the unsaturated part.

Although significant understanding of swash groundwater dynamics has been gained, experiments are limited because they are heavy to deploy, instruments lack spatio-temporal resolutions and measurements are quite intrusive [1,2]. Then, numerical models are needed to complete experimental insights. Even though extensive modelling effort has been provided over the last two decades, the proposed models [3,[4][5][6] are mostly based on Darcy's theory or horizontal dynamics (Dupuit-Forchheimer assumption). Thus, their scope remains limited since they ignore partial saturation and capillarity effect which are essential in fine-grained sand beaches. Indeed, field experiments demonstrated the presence of a circulation cell with vertical head gradients in sandy beaches [1]. To tackle these issues, the present study aims to model wave-resolved variablysaturated groundwater flow based on Richards' * Corresponding author: jean-baptiste.clement@fs.cvut.cz equation. Up to now, there are very few attempts to implement wave-forced Richards' equation [START_REF] Caviedes-Voullième | Numerical simulation of groundwatersurface interactions by external coupling of the 3D Richards equation and the full 2D shallow-water equations[END_REF].

The simulation of swash beach groundwater is challenging because the problem holds a wide range of space/time scales. Indeed, on one hand, waves have fast dynamics while groundwater is slow and on the other hand, swash infiltrations/exfiltrations have local effects while cross-beach gradients affect the whole beach. A numerical strategy has been developed in [START_REF] Clément | [END_REF] to solve efficiently Richards' equation. The resulting code, called Rivage, is used in this study to simulate waveresolved beach groundwater dynamics.

The first section deals with the model problem based on Richards' equation. Then, a brief description of the numerical methods used to solve Richards' equation is presented. The next section is dedicated to the results. A comparison is made with BARDEX II experiments. Finally, some conclusive remarks are given.

Model problem

The modelling of wave-forced groundwater flows in unsaturated porous media is introduced.

Richards' equation

Richards' equation is a non-linear degenerate parabolic equation to describe flows in variably-saturated porous media. Both the saturated and unsaturated zones are modelled. Yet, Richards' equation considers only the water phase which makes it competitive to simulate compared to full two-phase flow models. Richards' equation is based on the assumption that air phase is continuously-connected with the atmosphere and neglects inertial effects.

The Richards' equation under mixed formulation [9] is written in terms of hydraulic head ℎ = 𝜓 + 𝑧 [L]:

𝜕 𝑡 𝜃(ℎ -𝑧) -𝛻 ⋅ (𝑲(ℎ -𝑧)𝛻ℎ) = 0, ( 1
)
where 𝜓 is the pressure head [L], 𝜃 the water content [-], 𝑲 the hydraulic conductivity [L⸱T -1 ] and 𝑧 the elevation [L]. The saturated (𝜓 ≥ 0) and unsaturated (𝜓 < 0) zones are separated by the water table (𝜓 = 0). The capillary fringe is the unsaturated part almost entirely filled by water, just above the water table.

Richards' equation needs two constitutive laws to be solved: one for the water content and one for the hydraulic conductivity. The water content is described in terms of effective saturation 𝑆 e [-] and the tensor of hydraulic conductivity is supposed to react to pressure head identically for each space direction:

𝜃(𝜓) = 𝜃 s + (𝜃 s -𝜃 r )𝑆 e (𝜓), (2) 𝑲(𝜓) = 𝑲 𝐬 𝐾 r (𝜓), (3)
where 𝜃 s is the saturated water content [-], 𝜃 r the residual water content [-], 𝑲 𝐬 is the saturated hydraulic conductivity tensor [L⸱T -1 ] and 𝐾 r the relative hydraulic conductivity [-]. These two hydraulic properties have two different behaviours which explains the degeneracies of Richards' equation:

𝑆 e (𝜓) = { 1 if 𝜓 ≥ 0, 𝑆 e ⋆ (𝜓) otherwise, (4)
𝐾 r (𝜓) = { 1 if 𝜓 ≥ 0, 𝐾 r ⋆ (𝜓) otherwise. ( 5
)
𝑆 e ⋆ and 𝐾 r ⋆ are monotonic increasing functions of pressure head in the unsaturated zone. In this paper, the Van Genuchten-Mualem relations [10,11] are used:

𝑆 e ⋆ (𝜓) = (1 + (𝛼|𝜓| 𝑛 ) -𝑚 , ( 6
) 𝐾 r ⋆ (𝜓) = 𝑆 e ⋆ 0.5 (𝜓)(1 -(1 -𝑆 e ⋆ 1 𝑚 ⁄ (𝜓)) 𝑚 ) 2 , ( 7
)
where 𝛼 denotes a parameter [L -1 ] linked to air entry pressure inverse, 𝑛 > 1 a pore-size distribution parameter [-] and

𝑚 = 1 - 1 𝑛 [-].

Wave-driven boundary conditions

Classical boundary conditions can be applied to Richards' equation: a Dirichlet boundary condition enforces the hydraulic head and a Neumann boundary condition enforces the flux.

In addition, a specific boundary condition, called seepage, can be used for Richards' equation to model the interaction of porous media flow with atmosphere. This seepage boundary condition works as an outflow condition. If the porous medium is saturated, then the water pours out at atmospheric pressure. If the porous medium is unsaturated, then the water is prevented to go out. This condition can be written under many formulations but it can be viewed as a switch between a Dirichlet (prescribed zero pressure head) and a Neumann (prescribed zero flux) boundary conditions according to the state of saturations of the porous medium. Then, seepage can be interpreted as a nonlinear Robin boundary condition. For this study, the seepage boundary condition is treated inside the nonlinear iterative scheme according to the previous solution guess at a local level of the numerical scheme, as described in Clément et al. [START_REF] Clément | [END_REF]. This technique needs no restrictive a priori assumption on the seepage face.

In order to take into account the waves, a dynamic boundary condition is built to force the Richards' equation. It combines a Dirichlet and a seepage boundary condition. The former applies the hydraulic head induced by the water column wherever the swash tongue floods the beach. The latter is applied to the remaining part of the beach, beyond the swash tip. Thereby, the waves forcing condition allows the swash tip and the water table to be disconnected.

The surface water is computed by the open-source SWASH code which solves the nonlinear shallow water equations including non-hydrostatic pressure [12]. All parameters being kept by default, this wave-resolving model is used to get the bottom pressure which serves to monitor the Dirichlet boundary condition in space and time. From a technical point of view, the SWASH data are adapted to the groundwater model by performing linear interpolation of the space-time grids. The position of the swash tip is also provided to make explicitly the switch between the Dirichlet and seepage boundary conditions.

Numerical methods

Even though Richards' equation is widely used in the hydrogeology field, it remains challenging to solve. Indeed, due to the behaviour of hydraulic properties, nonlinear convergence is difficult to achieve and can even fail [9]. In addition, the solution of Richards' equation is known to exhibit spurious oscillations because of the degeneracies. Typically, an undershoot can appear ahead of a sharp wetting front propagating into an initially dry soil. These drawbacks make Richards' equation costly to compute [9]. In the case of wave-driven problems, the simulation of successive rapidly-varying infiltrations is demanding. Thus, a numerical strategy has been developed to alleviate these issues in Clément et al. [START_REF] Clément | [END_REF]. The main tools are presented briefly hereinafter.

Space discretization of Richards' equation (1) is done by a discontinuous Galerkin (DG) method called IIPG (Incomplete Interior Penalty Galerkin) because this formulation remains simple. Extensive introduction of DG methods can be found in the Rivière's textbook [START_REF] Rivière | Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations[END_REF]. The implicit Euler scheme is used for time discretization because it shows a wide region of stability needed for the Richards' equation known to be stiff. Linearization is achieved through a fixed-point method. It is linearly convergent while Newton-Raphson method is quadratically convergent but the former is more robust since it is not sensitive to the initial guess. In addition, an adaptive strategy based on a weighted DG framework and local mesh refinement is used to help with the solving of Richards' equation, see [START_REF] Clément | [END_REF].

The wave-forced Richards' equation-based model is used to assess water flow rates through an experimental beach barrier under different conditions.

Experimental and numerical set-ups

The BARDEX II project is a set of large-scale experiments conducted in July 2012 at the Delta Flume in the Netherlands [1,[START_REF] Turner | [END_REF]. They focus on the groundwater dynamics in a sand barrier under controlled laboratory conditions. Figure 1 Six experimental cases are selected to assess the effects of waves and cross-barrier gradients on the groundwater dynamics. Parameters are compiled in Table 1 where 𝐻 s is the significant wave height and 𝑇 p is the peak period. Each case is a run of 300 s. The barrier sand has been characterized in [2]. In the present study, the relations ( 6) and ( 7) are used with hydraulic parameters from a similar sand found in [START_REF] Benson | Estimating van Genuchten Parameters α and n for Clean Sands from Particle Size Distribution Data[END_REF] (Vail sand): 𝛼 = 4.6 m -1 , 𝑛 = 5.14, 𝜃 s = 0.41, 𝜃 r = 0.03 and 𝑲 𝐬 = 8 × 10 -4 m⸱s -1 . The SWASH model provides the free surface forcing on the beach face. The remaining boundary conditions for the simulation are similar as described in [3]. Initialization of groundwater is done in a such a way to match the initial state reached by the experimental runs described in [START_REF] Turner | [END_REF].

Comparison of water flow rates through the barrier

From BARDEX II experiments, Turner et al. [START_REF] Turner | [END_REF] calculated the averaged cross-barrier fluxes at the vertical cross-sections near the sea and the lagoon, as shown in Figure 1. These horizontal averaged flow rates were also computed from the numerical simulations of the Richards' equation-based model. The results are summarised in Table 2. Experimental and numerical values differ within a factor 2-3 which is reasonable in the field of hydrogeology [START_REF] Turner | [END_REF] and supports the numerical estimates from the present model. Besides, one should note that experimental results only account for flows in the saturated part unlike the numerical model. When there is no wave, horizontal fluxes are driven by the gradients induced by the difference of sea and lagoon level. For the case A6, experimental fluxes are not negligeable which indicates that the steady state was not reached as expected. Under waves action, the horizontal flux at sea is increased and it is seaward irrespective to the lagoon level. It shows that infiltration induced by waves are powerful enough to drive flows in the lower part of the swash zone. In order to assess the effect of waves in the swash zone, the numerical simulations are used to compute normal fluxes through a control plane linking and closing the upper part of the sea and lagoon crosssections, as shown in Figure 1. Results are presented in the Table 3. Indeed, they show infiltrations are increased with waves action. Figures 2, 3 and 4 bring insights about the repartition of averaged inflow/outflow in the upper part of the barrier under waves action. They confirm that the lagoon has limited influence. However, waves establish over time a circulation cell with infiltration/exfiltration respectively in the upper/lower part of the swash zone, which supports experimental observations [1,[START_REF] Turner | [END_REF]. For the cases A4w and A6w, infiltrations are important enough to explain the seaward horizontal flux. For the case A2w, infiltration is not dominant but the high lagoon level explains then the seaward horizontal flux.

Conclusion

In this paper, a Richards' equation-based model from the Rivage code is used to simulate wave-driven beach groundwater flows. Numerical results are compared against the large-scale BARDEX II experiments. A focus is made on the flow rates through the barrier. The difference between sea and lagoon water levels induces horizontal head gradients which rule the overall barrier groundwater dynamics. Nevertheless, waves generate infiltrations/exfiltrations beneath the swash zone which affect locally the beach saturation and produce vertical flow. These results highlight the establishment of a groundwater circulation cell as swash cycles recur.

Future studies need to evaluate the competition of horizontal and vertical head gradients according to additional parameters (types of waves and beaches) to see the effects on the circulation cell and sediments.

The Czech Technical University in Prague supported this work under the "CTU Global Postdoc Fellowship program".

  represents the experimental set-up. The sand barrier is 4.5 m high and 5 m wide. The barrier profile has five sections: (i) a concrete toe of slope 1:10 (24<X<29 m), (ii) a horizontal section (29<X<49 m), (iii) a beach face of seaward slope of 1:15 (49<X<109 m), (iv) a horizontal crest of height 4.5 m (109<X<114 m) and (v) a landward slope of 1:5 (114<X<124 m). A permeable retaining wall separates the barrier from a 10 m long lagoon.

Fig. 1 .

 1 Fig. 1. Description of the experimental set-up for the BARDEX II cases. The mean water level (MWL) at sea constant while the lagoon MWL can be kept higher (A2), lower (A4) or same (A6) level. The green/red/violet lines indicate respectively the sea/swash/lagoon control planes for the water flow rate.

Table 2 .

 2 Averaged flow rates through the sea/lagoon vertical control planes shown in Figure1. Positive/negative flow rates are respectively landward/seaward. Experimental results from[START_REF] Turner | [END_REF] are in blue and numerical results are in red.

Fig. 2 .

 2 Fig. 2. Averaged surface flow rate (normal) along the swash control plane in the case A2w (sea level < lagoon level) from numerical results.

Fig. 3 .

 3 Fig. 3. Averaged surface flow rate (normal) along the swash control plane in the case A4w (sea level > lagoon level) from numerical results.

Fig. 4 .

 4 Fig. 4. Averaged surface flow rate (normal) along the swash control plane in the case A6w (sea level = lagoon level) from numerical results.

Table 1 .

 1 BARDEX II experimental cases.

	Case	𝐻 s (m)	𝑇 p (s)	MWL sea (m)	MWL lagoon (m)
	A2	-	-	3	4.3
	A2w	0.8	8	3	4.3
	A4	-	-	3	1.75
	A4w	0.8	8	3	1.75
	A6	-	-	3	3
	A6w	0.8	8	3	3

Table 3 .

 3 Averaged flow rates through the swash control planes shown in red in Figure1from the numerical results.Negative flow rates are inflows.

	Case	Swash control plane (m 3 ⸱s -1 )	Case	Swash control plane (m 3 ⸱s -1 )
	A2	-1.79 × 10 -3	A2w	-2.32 × 10 -5
	A4	-6.64 × 10 -6	A4w	-1.02 × 10 -3
	A6	-7.73 × 10 -15	A6w	-9.03 × 10 -4


Anne-Laure Couderc
email: anne-laure.couderc@ap-hm.fr

Laetitia Ninove

Emilie Nouguerède

Dominique Rey

Marina Rebroin

Aurélie Daumas

Pascale Tomasini

Laurent Greillier

Sebastien Salas

Florence Duffaud

Laetitia Dahan

Muriel Duluc

Marie-Eve Garcia

Johan Pluvy

Solène Chaléat

Laure Farnault

Geoffroy Venton

Toscane Fourié

Elif Nurtop

Xavier De Lamballerie

Patrick Villani

Remi Charrel

Florian Correard

Acceptance, efficacy, and safety of COVID-19 vaccination in older patients with cancer

Keywords: COVID-19, Aged, Vaccination, Drug-Related Side Effects and Adverse Reactions, Medical Oncology, Geriatric assessment Respiratory Syndrome Coronavirus-2, CGA: Comprehensive Geriatric Assessment, CMR: Comprehensive Medication Reconciliation, IgG: Immunoglobuline G, ELISA: enzyme-linked immunoassay, BMI: Body Mass Index, ADL: Activities of Daily Living, IADL: Instrumental Activities

Introduction

Older frail people are more susceptible to severe forms of than the rest of the population; the infection rate is higher and outcomes poorer, in particular for those with comorbidities such as hypertension, diabetes, cancer, or cardiological and respiratory diseases [START_REF] Yang | Clinical course and outcomes of critically ill patients with SARS-CoV-2 pneumonia in Wuhan, China: a single-centered, retrospective, observational study[END_REF][START_REF] Aw | Association of frailty with mortality in older inpatients with Covid-19: a cohort study[END_REF]. In patients with cancer, COVID-19 has negative consequences on treatment delays and increases the mortality rate [START_REF] Harris | COVID-19 and cancer research[END_REF][START_REF] Robilotti | Determinants of COVID-19 disease severity in patients with cancer[END_REF][START_REF] Mehta | Case Fatality Rate of Cancer Patients with COVID-19 in a New York Hospital System[END_REF]. In this context, the COVID-19 vaccination campaign that began in France on December 27, 2020, primarily targeted the eldest people and then patients being treated for cancer [START_REF] Has | Stratégie de vaccination contre le Sars-Cov-2 -Recommandations préliminaires sur la stratégie de priorisation des populations à vacciner[END_REF][START_REF] Corti | SARS-CoV-2 vaccines for cancer patients: a call to action[END_REF]. The European Society of Medical Oncology (ESMO), the International Society of Geriatric Oncology (SIOG), and the French-Speaking Society of Geriatric Oncology (SoFOG) rapidly recommended COVID-19 vaccination in patients and older patients treated for cancer [START_REF] Battisti | Adapting care for older cancer patients during the COVID-19 pandemic: Recommendations from the International Society of Geriatric Oncology (SIOG) COVID-19 Working Group[END_REF][START_REF] Esmo | ESMO Statements for vaccination against COVID-19 in patients with cancer[END_REF][START_REF] Sofog | Recommandations de la SoFOG en termes de vaccination contre le SARS-CoV-2 chez les patients âgés traités pour un cancer[END_REF]. The particular severity of COVID-19 in frail older patients and patients with cancer has led to the inclusion of these populations in clinical trials in which they are usually poorly represented [START_REF] Talarico | Enrollment of elderly patients in clinical trials for cancer drug registration: a 7-year experience by the US Food and Drug Administration[END_REF].

In addition to its effectiveness, one of the other major challenges of vaccination is its acceptance by the population. The first data on vaccination in cancer patients stated a low acceptation rate [START_REF] Barrière | Acceptance of SARS-CoV-2 vaccination among French patients with cancer: a cross-sectional survey[END_REF][START_REF] Gustafson | Influence of immune aging on vaccine responses[END_REF] and at best, a mild intention rate for the COVID-19 vaccine [START_REF] Crooke | Immunosenescence and human vaccine immune responses[END_REF][START_REF] Polack | Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine[END_REF]. The very first data available on the intended acceptance of COVID 19 vaccination in French patients with cancer showed that only half patients intended to be vaccinated as soon as the vaccine was available [START_REF] Barrière | Acceptance of SARS-CoV-2 vaccination among French patients with cancer: a cross-sectional survey[END_REF].

Given the polemic surrounding COVID-19 vaccine, especially in the beginning of the vaccination campaign, and the observed worse outcomes in COVID-19 among older patients or cancer patients, older cancer patients' COVID-19 vaccination acceptance was and still is, crucial to limit adverse outcomes for this frail population.

However, the efficacy of vaccines in older patients is still unclear because of immunosenescence, including the reduction of both qualitative and quantitative aspects of the immune system available to respond to a vaccine [START_REF] Gustafson | Influence of immune aging on vaccine responses[END_REF][START_REF] Crooke | Immunosenescence and human vaccine immune responses[END_REF]. A study on BNT162b2, a lipid nanoparticle-formulated, nucleoside-modified RNA COVID-19 vaccine, showed 95% efficacy seven days after the second dose in a population including 42% of older adults and 3.7% of adults with cancer [START_REF] Polack | Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine[END_REF]. In patients treated with anti-cancer agents, this vaccine could interfere with cancer treatment through a molecular phenomenon known as the permeation and retention effect [START_REF] Fanciullino | COVID-19 vaccine race: watch your step for cancer patients[END_REF]. Moreover, patients treated with immunotherapy could, in theory, display an exaggerated inflammatory immune response after vaccination. Despite this, vaccination appears to be the main tool to prevent severe outcomes and hospital admissions due to COVID-19.

From January 2021, we offered COVID-19 vaccination to all patients over 70 years old with cancer attending the geriatric oncology center for geriatric advice before initiation of oncological treatment. The main objective was to evaluate the acceptance of COVID-19 vaccination by older patients with cancer. The secondary objective concerned vaccine safety, reactogenicity, and efficacy in the two months following the first dose.

Materials and methods

Study Design and Participants

This research is a study focused on vaccination prescription before oncological treatment, derived from the ongoing prospective observational cohort study "ChimioAge", initiated in January 2017 at Marseille University Hospital (NCT03960593) [START_REF] Couderc | Medication Reconciliation Associated with Comprehensive Geriatric Assessment in Older Patients with Cancer: ChimioAge Study[END_REF]. The ChimioAge cohort aims to collect geriatric, oncological and drug prescriptions data of all consecutive patients aged 70 years or over with cancer, referred to our geriatric oncology center for geriatric advice before initiation of treatment. All patients benefit from a Comprehensive Geriatric Assessment (CGA) [START_REF] Mohile | Practical Assessment and Management of Vulnerabilities in Older Patients Receiving Chemotherapy: ASCO Guideline for Geriatric Oncology[END_REF] and a Comprehensive Medication Reconciliation (CMR) [START_REF] Scotte | Addressing the quality of life needs of older patients with cancer: a SIOG consensus paper and practical guide[END_REF][START_REF] Son | Pharmacist-led interdisciplinary medication reconciliation using comprehensive medication review in gynaecological oncology patients: a prospective study[END_REF][START_REF] Mekonnen | Pharmacy-led medication reconciliation programmes at hospital transitions: a systematic review and meta-analysis[END_REF].

From January 18, 2021, COVID-19 vaccination prescription was offered to all patients at the time of the CGA. Those who agreed received the BNT162b2 vaccine, which was administered intramuscularly in two doses 21 days apart, as part of the national vaccination campaign. Inclusion in the "vaccine survey" ended on May 7, 2021 (four months), when vaccination prescriptions were available in other centers (pharmacies or office of general practitioners or nurses) and when patients addressed for CGA were mostly vaccinated. Participants were followed up by telephone 60 days after receiving the first dose of the vaccine. Patients who were already vaccinated with a vaccine other than BNT162b2 were not eligible for the survey.

Geriatricians and pharmacists collected the data. Patients were included in the study after providing their written informed consent. The study protocol was approved by an Ethics Committee (CPP Ouest IV -Nantes registered under number 61/18_3).

Data collection

The CGA, including assessment of autonomy, cognitive status, nutritional status, mobility, handgrip strength and polypharmacy (minimum of five prescribed medications) was assessed by both validated psychometric scales and clinical assessment, and has been previously detailed [START_REF] Couderc | Medication Reconciliation Associated with Comprehensive Geriatric Assessment in Older Patients with Cancer: ChimioAge Study[END_REF]. Information about demographic characteristics and lifestyle (age, gender, accommodations and presence of a caregiver) were also collected. Cancer site and stage, treatment, hospitalizations, and death were obtained from the medical records. Among data directly related to CMR, only side effects of the vaccination collected during the CMR follow-up were analyzed.

Vaccine uptake, side effects, and efficacy

During the geriatric day hospitalization, patients received a CGA conducted by a geriatrician and a CMR conducted by a pharmacist. The CMR was usually conducted prior to the CGA and consisted of an in-depth interview with the patient about the current treatment and any self-medication or dietary supplements taken by the patient. During the vaccination campaign, the geriatricians and the pharmacists acted in synergy to explain the benefits and risks of COVID-19 vaccination.

Vaccination was proposed at the end of the CGA, people who agreed received the first dose of the vaccine. Those who refused vaccination were asked about the reasons for not accepting or contraindications. A hospital pharmacist called all the patients included 60 days after administration of the first dose or refusal. The pharmacist collected reactogenicity and safety data from all the vaccinated patients 21 days after the first injection for the first vaccine dose (at the time of the second injection), and 60 days after the first injection for the second vaccine dose (last follow-up). Dates and reasons for hospitalizations, as well as COVID-19 infection dates, were collected from vaccinated and unvaccinated patients.

Laboratory analyses

Among the vaccinated group, 22 patients agreed to have their serum samples tested for quantitative detection of anti-SARS-Cov-2 spike (S1) IgG antibodies (Euroimmun®, Luebeck, Germany) before the second vaccine dose. All samples with an ELISA ratio ≥ 0.7, neutralizing antibodies against SARS-Cov-2 were detected using a virus neutralization test (VNT100) [START_REF] Gallian | Lower prevalence of antibodies neutralizing SARS-CoV-2 in group O French blood donors[END_REF]. Anti-S1IgG was expressed in standardized units (binding antibody units per mL) with a positive threshold of 35.2 BAU/mL.

Statistical analysis

A descriptive analysis was performed for demographic, oncological, geriatric, and treatment characteristics of our population using headcounts and percentages for discrete data, as well as mean values plus or minus the standard error and the interval between the minimum and maximum values for continuous data. A comparative analysis of patients who accepted versus those who refused the vaccine was performed. The Chi-squared test was used to analyze discrete data whereas Student's t-test was used to analyze continuous variables. Concerning the serology testing, we compared the positive and negative serology results. All the statistical analyses were performed using SPSS software (version 17.0).

Results

Between January 18, 2021 and May 7, 2021, 150 patients with cancer attending the day-care hospital for a CGA were offered vaccination against COVID-19 with the BNT162b2 vaccine and were included in the survey. The study sample consisted of 58 (38.7%) women and 92 (61.3%) men, with a mean age of 81 years (range 70-94). The most frequent primary tumors were digestive (n=44; 29.4%) and thoracic cancers (n=27; 18%). The socio-demographic, oncological, and geriatric characteristics of the patients are detailed in Table 1.

All patients were offered the BNT162b2 vaccine, and all were expected to have their cancer treatment within weeks of vaccination. Sixty two percent (n=93) of the patients agreed to be vaccinated (79 patients (52.7%) accepted right away, 14 patients (9.3%) initially refused but accepted upon reflection)), 20.7% (n=31) were already vaccinated, and 17.3% (n=26) refused. Among those who refused, four were scared of the side effects of the vaccine, seven were against vaccination, ten were undecided at the time of the proposal, four had already been infected with COVID-19, and the last one had an ongoing infection but not COVID-19 (Figure 1). Patients who accepted vaccination and those who refused did not differ in terms of socio-demographic, oncological, and geriatric characteristics (Table 2). A total of 82 patients out of the 93 who received the first dose returned for the second injection. Few of them (n=13; 15.9%) reported mild side effects after the first vaccine injection, mostly arm pain at the injection site (Table 3). After the second injection, 23.4% of patients (n=18) described side effects, mainly arm pain and fatigue. Taking into account those already vaccinated at the time of the study, the acceptance rate of the vaccine was 82.7% and the complete vaccination rate (two doses) reached 75.3%.

A total of eight COVID-19 cases were identified during follow-up: five (5.2%) cases in the vaccine group and three (18.8%) cases in the non-vaccinated group. Moreover, 16 patients died during follow-up: 14 in the vaccinated group and two in the non-vaccinated group. In the vaccinated group, one death was COVID-19-related (contamination one week after the first vaccine injection, death 40 days later), and 13 were cancer-related. In the non-vaccinated group, the causes of death were unknown for the two patients.

We analyzed responses to mRNA vaccination against COVID-19 among 22 patients, 21 days after the first dose of vaccine.

We found specific antibodies to the SARS-CoV-2 spike protein in 15 patients (68.2%). Neutralizing antibodies against SARS-Cov-2 were detected in three patients using VNT100.

The seven patients with a negative serology were more likely to be men, older, with metastatic cancer, and on multiple medications (Table 4).

Discussion

This single-center study reports acceptance of the COVID-19 vaccine by patients ≥ 70 years with cancer before initiation of oncological treatment. In our cohort, 82.7% of patients agreed to be vaccinated against COVID-19 and 75.3% received the two recommended BNT162b2 vaccine injections. Less than one in four vaccinated patients reported side effects, mainly injection site pain and fatigue. No serious side effects were reported.

Our results show a much higher acceptance rate of vaccination in the older population with cancer than expected given the results of opinion surveys carried out at the end of 2020 in France. A nationwide study showed that only 60% of the population aged over 65 years were considering vaccination against COVID-19 [START_REF] Coviprev | Comment évolue l'adhésion à la vaccination et aux gestes barrières contre la Covid-19 ? Résultats de la vague 25 de l'enquête CoviPrev[END_REF]. A cross-sectional survey on acceptance of COVID-19 vaccination among patients with cancer reported that only 53.7% intended to be vaccinated as soon as the vaccine was available. In the latter, the median age was 67 years and 47% of participants were undergoing active treatment against cancer [START_REF] Barrière | Acceptance of SARS-CoV-2 vaccination among French patients with cancer: a cross-sectional survey[END_REF]. However, the reported rate of vaccination refusal was to that observed in our study (17%) [START_REF] Barrière | Acceptance of SARS-CoV-2 vaccination among French patients with cancer: a cross-sectional survey[END_REF].

Moreover, the percentage of people vaccinated (75.3%) was also higher in our study than observed in the French old population at the same date: in France on May 20, 2021, only 54% of people ≥ 70 years had received full vaccination regardless of the vaccine type [START_REF]Données relatives aux personnes vaccinées contre la Covid-19 (VAC-SI) -data[END_REF]. Vaccination was proposed by the geriatrician in the context of CGA, with time available to answer any questions the older patients and/or their caregivers had. In addition, and complement the geriatrician efforts, the pharmacists in charge of the CMR were also present to explain to the patients the benefits and risks of vaccination and reassured them on any fears they may have. The combination of geriatric and pharmacological assessment has certainly helped to improve the acceptance rate of the vaccine among hesitant older people, although it is impossible to distinguish the respective impact of the physician and the pharmacist on the elderly person's choice. In addition, patients did not have to wait for an appointment or come back later for their first injection, which was easily accessible on the same day as the CGA. This convenience may have made a big difference for patients who often have limited mobility. We assume that both the time spent on correctly answering all the patients' questions and fears about the efficacy and side effects of the vaccine, as well as the pragmatic approach, were instrumental in increasing the acceptance rate. Of the remaining 26 patients who refused vaccination, five had reasonable reasons (were recently or currently infected with COVID-19). The last twenty-one patients were not vaccinated during the study (even after 60 days of follow-up).

According to our results, 16% and 23% of patients reported mild or moderate side effects after the first and second vaccine injections, respectively, as previously reported in adults aged over 70 years without cancer [START_REF] Anderson | Safety and Immunogenicity of SARS-CoV-2 mRNA-1273 Vaccine in Older Adults[END_REF]. In contrast, the frequency of side effects in our study was lower than the 54% reported after the first dose in patients with cancer [START_REF] Monin | Safety and immunogenicity of one versus two doses of the COVID-19 vaccine BNT162b2 for patients with cancer: interim analysis of a prospective observational study[END_REF]; this discrepancy may be due to the fact that we proposed vaccination before cancer therapy was initiated, whereas it was done during the oncological treatment in Monin et al. [START_REF] Monin | Safety and immunogenicity of one versus two doses of the COVID-19 vaccine BNT162b2 for patients with cancer: interim analysis of a prospective observational study[END_REF]. Despite our cohort being too small to evaluate vaccine efficacy, the proportion of patients who had COVID-19 in the non-vaccinated group was three times higher than in the vaccinated group. In the study by Bernal et al., vaccination with one dose of BNT162b2 in 156 930 older adults was associated with a significant reduction in symptomatic COVID-19 and further protection against severe disease (43% reduced risk of emergency hospital admission and 51% reduced risk of death) [START_REF] Bernal | Effectiveness of the Pfizer-BioNTech and Oxford-AstraZeneca vaccines on covid-19 related symptoms, hospital admissions, and mortality in older adults in England: test negative case-control study[END_REF]. Other studies showed poor efficacy of one dose of the BNT162b2 vaccine in old patients with cancer but a substantial serological response after 2 injections [START_REF] Barrière | Acceptance of SARS-CoV-2 vaccination among French patients with cancer: a cross-sectional survey[END_REF][START_REF] Monin | Safety and immunogenicity of one versus two doses of the COVID-19 vaccine BNT162b2 for patients with cancer: interim analysis of a prospective observational study[END_REF]. However, the correlation between the serological response to COVID-19 vaccination and clinical protection is still not fully documented [START_REF] Leshem | Population immunity and vaccine protection against infection[END_REF].

The high frequency of digestive and lung cancers in our study is consistent with our usual activity but can also be explained by a kind of priority given to certain patients by oncologists, whether they are patients at risk because of pre-existing inflammatory lung disease or patients scheduled to receive immunotherapy. [START_REF] Luo | Impact of PD-1 Blockade on Severity of COVID-19 in Patients with Lung Cancers[END_REF].

An important limitation of this study is the small number of quantitative detections of the anti-SARS-Cov-2 spike (S1) IgG antibodies made before the second vaccine dose and the lack of testing carried out after the second dose, which prevents us from drawing any conclusions regarding the effectiveness of the vaccine. Moreover, two vaccinated patients and four non-vaccinated patients were lost to follow-up at the end of the survey, and causes of death were unknown for the two nonvaccinated patients who died during the survey. The implementation of the study at the very beginning of the vaccination campaign and its termination after 60 days due to changes in national vaccination strategies may have also led to an overestimation of vaccine hesitancy in our study. Furthermore, we were not able to follow up on possible changes of mind in people who had refused vaccination, as the oncological follow-up of these patients was carried out in departments geographically distant from ours. In addition, it was a monocentric study including patients with all types of cancers and systemic treatments.

Conclusion

Our survey among older patients with cancer showed a high acceptance rate of COVID-19 vaccination in this population, probably linked to the choice of proposing vaccination in the context of the comprehensive geriatric assessment. COVID-19 vaccination carried out before initiation of cancer treatment was better tolerated than previously described and, of those who were fully vaccinated, only 5% were infected with COVID 19 but none developed severe forms. This suggests the possible benefit of not vaccinating at the same time as systemic cancer treatment when possible and organizing vaccination campaigns at the very beginning of oncological management. Larger studies to measure the durability and effectiveness of vaccine protection should be correlated with the BAU/VNT measurements before general rules can be implemented.

Figure 1 :

 1 Figure 1: Study Flow Chart

Table 1 :

 1 Characteristics of the population (n=150 old patients with cancer)

			Total population
	Characteristics		N or	% or
			Mean±SD	[min-max]
	Gender
			58	38.7
		Women
		Men	92	61.3
	Age		81±0.5	[70-94]
		70-75	29	19.3
		76-80	45	30.0
		81-85	37	24.7
		> 85	39	26.0
	Accommodation Home		133	88.6
	Care facility	10	2.0
	Nursing home	3	6.7
		Other	4	2.7
	Living alone		33	22.0
	Caregiver present		127	84.7
	Polypharmacy *		96	64.0
	Cognitive impairment (n=149)		65	43.6
	Depression risk		50	33.3
	Malnutrition		60	40.3
	BMI (Kg/cm²)	25.0±0.4	[16.2-36.8]
	Albumin (g/L)	38.7±0.5	[25.0-65.0]
	Functional status (n=149)
	Independent	64	43.0
	Dependent in ADL or IADL	31	20.8
	Dependent in ADL and IADL	54	36.2
	Mobility
	Impaired TUG	104	69.3
	Impaired OLBT	135	90.0
	Impaired gait speed	92	61.7
	Falls in the 3 previous months	20	13.3
	Handgrip strength impairment (n=149)	58	38.9
	G8 impairment		131	87.3
	ECOG-PS (n=149)	0-1	65	43.6
		2-4	84	56.4
	Stage IV (n=148)		56	37.8
	Cancer type
	Digestive	44	29.4
		Thoracic	27	18.0
	Urological	20	13.3
		Prostatic	15	10.0
		Skin	14	9.3
	Head and Neck	12	8.0
	Breast and gynecological	12	8.0
	Hematological	4	2.7
		Other	2	1.3
	BMI: Body Mass Index; ADL: Activities of Daily Living; IADL: Instrumental Activities of Daily Living; TUG: Timed Up and Go test; OLBT: One Leg
	Balance Test; ECOG-PS: Eastern Cooperative Oncology Group-Performance status
	*at least 5 prescribed medications

Table 2 :

 2 Comparative analysis of geriatric and oncological characteristics between vaccinated and non-vaccinated patients -n=146

			Vaccinated (n=124)	Non-vaccinated (n=22)
	Characteristics		N or	% or	N or	% or	p-Value
			Mean±SD	[min-max]	Mean±SD	[min-max]
	Gender	Women	47	37.9	9	40.9	0.815
		Men	77	62.1	13	59.1
	Age		81±0.5	[70-94]	81±1.4	[70-94]	0.688
		70-75	24	19.4	4	18.2	0.716
		76-80	37	29.8	6	27.2
		81-85	32	25.8	4	18.2
		> 85	31	25.0	8	36.4
	Accommodation Home		111	89.6	18	81.9	0.307
	Care facility	7	5.6	3	13.6
	Nursing home	2	1.6	1	4.5
		Other	4	3.2	-	-
	Living alone		29	23.4	4	18.2	0.784
	Caregiver present		104	83.9	19	86.4	1.000
	Polypharmacy*		80	64.5	12	54.5	0.473
	Cognitive impairment (n=145)	53	43.1	9	40.9	1.000
	Depression risk		42	33.9	5	22.7	0.336
	Malnutrition		47	38.2	11	50.0	0.299
	BMI (Kg/cm²)	25.3±0.4	[16.2-36.1]	23.3±0.9	[17.1-36.8]	0.044
	Albumin (g/L)	38.8±0.5	[27.0-48.0]	38.1±2.3	[25.0-65.0]	0.761
	Functional status
	Independent	51	41.1	12	54.6	0.456
	Dependent in ADL or IADL	28	22.6	3	13.6
	Dependent in ADL and IADL	45	36.3	7	31.8
	Mobility
	Impaired TUG	89	71.8	12	54.5	0.133
	Impaired OLBT	112	90.3	20	90.9	1.000
	Impaired gait speed (n=145)	77	62.6	13	59.1	0.813
	Falls in the past 3 months	17	13.7	2	9.1	0.739
	Handgrip strength impairment (n=145)		49	39.8	8	36.4	0.817
	G8 impairment		108	87.1	19	86.4	1.000
	ECOG-PS (n=145)	0-1	54	43.9	10	45.5	1.000
		2-4	69	56.1	12	54.5
	Stage IV (n=144)		47	38.2	6	27.3	0.470
	Cancer type
	Digestive	35	28.2	8	36.4	0.512
	Thoracic	22	17.7	4	18.2
	Urological	19	15.3	1	4.5
	Prostatic	11	8.9	3	13.7
		Skin	13	10.5	1	4.5
	Head and Neck	8	6.5	4	18.2
	Breast and gynecological	11	8.9	1	4.5
	Hematological	4	3.2	-
		Other	1	0.8	-
	BMI: Body Mass Index; ADL: Activities of Daily Living; IADL: Instrumental Activities of Daily Living; TUG: Timed Up and Go test; OLBT:
	One Leg Balance Test; ECOG-PS: Eastern Cooperative Oncology Group-Performance status
	* At least 5 prescribed medications

Table 3 :

 3 Descriptive analysis of COVID-19 vaccine (BNT162b2) patient-reported side effects The 31 patients already vaccinated were excluded from this analysis. ⁑ Information collected at the time of the second injection (day 21 after the first injection) ⁂ Information collected at the end of follow-up (day 60 after the first injection)

		After first injection	After second injection
	Side effects (SE) ⁎	(n=82 respondents) ⁑	(n=77 respondents) ⁂
		n	%	n	%
	Absence of SE	69	84.0	59	76.6
	Presence of SE	13	15.9	18	23.4
	Local reactivity
	Arm pain	8	9.8	12	15.6
	Rash	2	2.4	-	-
	Systemic reactivity
	Fever	2	2.4	5	6.5
	Asthenia	5	6.1	10	13.0
	Headache	1	1.2	1	1.3
	Other	-	-	1	0.7

⁎

Table 4 :

 4 Comparative analysis of geriatric and oncological characteristics between vaccinated patients with positive versus negative serology, 21 days after first vaccine injection (n=22)

			Positive serology (n=15)	Negative serology (n=7)
	Characteristics		N or	% or	N or	% or
			Mean±SD	[min-max]	Mean±SD	[min-max]
	Women		6	40.0	2	28.6
	Age	70-80	7	46.7	2	28.5
		> 80	8	53.3	5	71.4
	Living at home		15	100	6	85.7
	Living alone		2	13.3	3	42.9
	Caregiver present		15	100	5	71.4
	Polypharmacy *		6	40.0	6	85.7
	Cognitive impairment		4	26.7	4	57.1
	Malnutrition		5	33.3	2	28.6
	BMI (Kg/cm²)	24.3±1.3	[16.5-33.3]	24.7±1.5	[20.1-30.4]
	Albumin (g/L)	41.1±1.1	[34.0-46.0]	37.1±1.7	[28.0-42.0]
	Functional status
	Independent	7	46.7	4	57.1
	Dependent in ADL or IADL	5	33.3	1	14.3
	Dependent in ADL and IADL	3	20.0	2	28.6
	Mobility
	Impaired TUG	12	80.0	5	71.4
	Impaired OLBT	13	86.7	7	100
	Impaired gait speed	10	66.7	4	57.1
		Falls	3	20.0	-	-
	Handgrip strength impairment	4	26.7	1	14.3
	G8 impairment		13	86.7	6	85.7
	ECOG-PS	0-1	8	53.3	4	57.1
		2-4	7	46.7	3	42.9
	Stage IV		4	26.7	3	50.0
	Cancer type
		Digestive	1	6.6	3	43.0
		Thoracic	4	26.7	-	-
		Urological	4	26.7	2	28.5
	Breast and gynecological	3	20.0	-	-
		Other	3	20.0	2	28.5

BMI: Body Mass Index; ADL: Activities of Daily Living; IADL: Instrumental Activities of Daily Living; TUG: Timed Up and Go test; OLBT: One Leg Balance Test; ECOG-PS: Eastern Cooperative Oncology Group-Performance status; NA: Not Applicable * At least 5 prescribed medications

Conflicts of interest

Availability of data and materials:

The data are available from the corresponding author upon reasonable request.