## 5 Results and Discussion
### Spectra behind Disks  
To study the redistribution of turbulence energy along the wake, the spectra obtained at different longitudinal positions for every disk are compared with the spectrum of the free decaying turbulence. Power Spectral Density (PSD) curves are calculated from only one measuring position at centreline, so to reduce the noise in the spectral curves, the time-series of each register are divided into eight non-overlapping blocks with an equal number of samples. Then, the PSD of all blocks are averaged to produce the curve at each longitudinal position. However, noise remains along the curves that make the comparison very difficult, so a smoothing procedure is needed to be performed. To this aim, an exponential moving average is used to filter the spectra computed at each longitudinal position (a rational transfer function is employed, see [55]). Hence, the spectra shown in the following figures have been processed with this technique, with the sole exception of that obtained from measurements without a disk, which was spatially averaged with results obtained at the other eight locations distributed crosswisely. As the spectra are calculated from data at a fixed location (sampled in time), the [PERSON] hypothesis is applied to transform the frequency spectra into a wavenumber spectra using \(\kappa_{1}=2\pi f/\left<U\right>\), where \(f\) is \(f_{acq}\) for measurements or \(f=1/\Delta t\) for the LES. In this way, it is possible to also compare with the PSD from the synthetic turbulence, which is calculated as the volume average of the spectra computed in the longitudinal direction. The results for the inflow Ti3 are shown in Figure 15. In the results without the AD, a constant decay of energy is observed as the flow moves downstream. The spectra from the synthetic box serve to mark the extension of the resolved wavenumbers (\(\kappa_{max}=\pi/\Delta=1571\) m\({}^{-1}\)) since the spatial resolution in the box is the same as in the LES. Note that the abrupt drop in the turbulence energy spectra is attributed to a combination of numerical diffusion and the limited spatial resolution [5]. In case of the disk \(C_{T}=0.42\), a gain in turbulence energy is seen immediately behind the disk, as the curves at \(-1D\) and \(1D\) are almost identical. A small decay of energy is observed at \(4D\) and, from there, an increase in turbulence energy around the highest levels (lowest \(\kappa\)). For the disk \(C_{T}=0.62\), the effects are accentuated, and the curves at \(4D\) are the only ones displaying a decay and yet only around the inertial range. The energy of the next two longitudinal positions, \(10D\) and \(14D\), increases for all wavenumbers, which represents an increment of about one order of magnitude at the lowest wavenumber, with respect to the levels displayed by the decaying turbulence without disks. Notably, the spectra of the last two positions seemingly exhibit an inertial range, characterized by the slope of \(-5/3\) in the decay rate. The results for the Ti12 inflow are shown in Figure 16. In this case, the spectra computed from experimental results are also included. The spectra obtained from measurements with disks extend to larger wavenumbers than in the cases without disk, due to the use of a different frequency in the low-pass filter. For the case without disks, the energy at the lowest wavenumbers obtained from the LES proves to decay less as it has been shown before. However, they display a steady decay that adjusts well to the characteristic slope of the inertial range, also discernable in the experimental results. These observations are analogous for the results with the disk \(C_{T}=0.45\). In contrast to the Ti3 inflow where energy is seen to increase beyond \(x=4D\) for the disk with the same porosity, here a reduction  
Figure 14: Vertical profiles of \(L_{1}\) behind the AD with inflow Ti12, disk \(C_{T}=0.45\) (**left**) and \(C_{T}=0.71\) (**right**). in the contribution of shear towards the increase of energy along the wake is observed.