## 5 Results and Discussion
### Turbulence Dissipation in the Wake  
In the LES computations, the dissipation shown corresponds to \(\varepsilon_{tot}=\varepsilon_{res}+\varepsilon_{\text{\tiny{GS}}}\). The dissipation is calculated from the HWA data using Equations (2) and (3), which was only available in the Ti12 case. Therefore, results of Ti3 are shown only for completeness in Figure 9, where it can be seen that, as before, differences between LES and RANS are small, as the curves differ only at \(x=2D\) where RANS predicts a higher dissipation within the shear layer. For the results with the Ti12 inflow in Figure 10, it is seen that, for the disk \(C_{T}=0.45\), the LES predictions compare well with measured values. For the disk \(C_{T}=0.71\), the measurements reveal a large increase of dissipation within the shear layer, compared to the data of computations with the lower thrust AD. Furthermore, at least within the three longitudinal positions available, measured  
Figure 8: Vertical profiles of \(k\) behind the disk \(C_{T}=0.45\) (**left**) and \(C_{T}=0.71\) (**right**), Ti12 case. Figure 7: Vertical profiles of \(k\) behind the disk \(C_{T}=0.42\) (**left**) and \(C_{T}=0.62\) (**right**), Ti3 case. Figure 9: Vertical profiles of \(\varepsilon\) behind the disk \(C_{T}=0.42\) (**left**) and \(C_{T}=0.62\) (**right**), Ti3 case. dissipation in the shear layer is more or less maintained. The computations with \(C_{T}=0.71\) also display a somewhat stronger mixing of turbulence from \(x=4D\), where dissipation becomes more uniform and less predominant in the shear layer. The RANS computations with the modified \(k-\varepsilon\) model of [PERSON] and [PERSON] have been previously shown capable of reproducing the turbulence level in the wake [17]. In the present comparison, it is seen that for the Ti3 inflow the agreement is very good for the disk \(C_{T}=0.42\) while it falls somewhat behind in the far wake of \(C_{T}=0.62\). However, in both cases, the agreement in the computed dissipation of RANS and LES is very good except for \(x=2D\). Interestingly, it is the vicinity of the disk where the \(k\)-\(\varepsilon\) is often corrected by adding dissipative terms to the \(\varepsilon\) equation to overcome the miscalculated turbulence stresses [49]. The results with the Ti12 show the opposite picture with regard to the estimation of \(k\), as the agreement with measurements becomes better only for farther distances from the disk. For the closest position, the turbulence level is overestimated (as it is in the LES) despite the drop of the turbulence production terms near the disk (\(x=2D\) is outside this region). Dissipation seems overestimated in the case of \(C_{T}=0.45\) when comparing to the measurements. This is less certain for the higher thrust disk, where at \(x=4D\) the peak value of dissipation seems equal to the measured one, but much smaller in the case of \(x=6D\). Notably, \(\varepsilon\) from RANS is always higher than any LES in the wakes of the Ti12 inflow. Previous work [49] has shown that, in the ABL, the \(k\)-\(\varepsilon\) model overestimates the dissipation around the disk when comparing with LES. This has been observed to occur even upstream of the disk, where \(\varepsilon\) has been seen to increase unlike computations of LES, where this value does not grow until \(0.5D\) downstream from the rotor. It should be remarked that [PERSON] and [PERSON] [17] showed that results with various turbulence closures (standard \(k\)-\(\varepsilon\), RNG, [PERSON] and [PERSON] model [48] and their own model) compare, in essence, equally well to the measurements, with no apparent advantage of their proposed correction to the \(k\)-\(\varepsilon\) model (although \(\varepsilon\) yielded by the different closures was not compared). The fact that all models compare well to measurements appears to contradict the otherwise inadequate results obtained in simulations of wakes in the ABL flow cited in that work.