## 3 Experimental Setup and Measurement Campaigns  
The measurements used in this work come from experiments performed in the Eiffel-type wind tunnel of the Prisme laboratory of the University of Orleans. The test section has a width and a height of 0.5 m and a length of 2 m. Two different grids were used to generate turbulence at the entrance of the test section, resulting in two different turbulence intensities. At a distance of \(x=0.5\) m from that grid, the reported values of turbulence intensity and integral lengthscale (measured at the centreline) were TI = 3% and \(L_{1}=0.01\) m as well as TI = 12% and \(L_{1}=0.03\) m. These two inflow cases are henceforward identified as Ti3 and Ti12, respectively. The streamwise position where these values are reported is referred to as the _target position_\(x_{D}\). Later, disks made of a metallic mesh were located at \(x_{D}\) to simulate the effect of the AD model (a porous surface) on the flow. Two disks were used, each with a diameter of \(D=0.1\) m but made with a different wire to produce different induction factors. The thrust coefficient \(C_{T}\) of each disk is calculated following the procedure presented by [13] and revisited by [17], based on the measurement of the velocity deficit in the wake. In total, six experimental cases are considered for this work as shown in Table 1. Complete details about the experimental setup, the measurement techniques as well as the characteristics of the flows generated by this wind tunnel can be found in [15; 31]. The data used in this work was obtained using two different techniques. Firstly, with the aim of obtaining time-series of the flow velocity, a Hot-Wire Anemometry (HWA) probe was located along vertical lines at \(x=3D\), \(4D\) and \(6D\) from the disk centre (the origin of the reference system \(x,y,z=0,0,0\) is set there). The probe moved along each vertical line between \(0\leq y/\text{D}\leq 1.5\), registering data at different steps (data recorded every \(0.1D\) is employed). A scheme of the measuring locations with respect to the experimental arrangement is shown in Figure 1. At each probe position, data was acquired with a sampling frequency of \(f_{acq}=2\) kHz during about 1 min. A low-pass filter was also used, with a cut-off frequency fixed at \(f_{c}=1\) kHz. The reference velocity during these measurements was \(U_{\infty}=3\) m/s. Of the measurements made with this technique, only the database corresponding to the cases of Ti12 is used in the comparisons shown here since the sampling rate was assessed to be too low for the turbulence scales of the Ti3 case. Due to this, HWA measurements from [16] are used to complement the experimental data for the comparison of the Ti3 case. These were \begin{table}
\begin{tabular}{c c c} \hline \hline
**TI [\%]** & \(L_{1}\) **[m]** & **Case** \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{0.01} & No-disk \\ \cline{3-3}  & & \(C_{T}=0.42\) \\ \cline{3-3}  & & \(C_{T}=0.62\) \\ \hline \multirow{3}{*}{12} & \multirow{3}{*}{0.03} & No-disk \\ \cline{3-3}  & & \(C_{T}=0.45\) \\ \cline{3-3}  & & \(C_{T}=0.71\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reference parameters of flow and disks used in the experiments. made using the same experimental setup as the other HWA measurements, with TI \(\simeq 3\%\) also at the target position but with \(U_{\infty}=20\) m/s and in consequence a higher Reynolds number. Secondly, a Laser-Doppler-Anemometer (LDA) was used to simultaneously measure two components of velocity \((u,v)\) with the main purpose of obtaining time-averaged information of the wake. Measurements behind the disks were made along the vertical directions at \(x=2D\), \(4D\), \(6D\), \(8D\) and \(10D\) from the disk centre. The recording positions were aligned in the vertical direction, performed in steps (generally) of \(0.1D\) between \(-1.5\leq y/D\leq 1.5\). For the Ti3 cases, the positions in the vertical direction where data is available vary slightly, but most of them are made in steps of \(0.1D\) between \(-1.0\leq y/D\leq 1.0\).