## 5 Results and Discussion  
Different mesh refinements have been tested at the rotor-wake region with actuator disk rotors and the \(k\)-\(\varepsilon\) turbulence model to achieve a mesh independent solution. In all cases, results at the far wake regions (\(>\)15 diameters) were not affected from local refinements at the wind farms area upstream. Solutions converged with residuals below \(10^{-4}\) for pressure and below \(10^{-6}\) for the turbulence parameters and the three velocity vectors.  
At the following pages results of the turbulence kinetic energy (TKE) and velocity deficits for the two cases of \(TI=8\%\) (Figures 5a and 6, Figures 8a and 9a) and \(TI=15\%\) (Figures 5b, 7, 8b and 9b) are presented.  
The TKE production k is compared against the expected ambient TKE production at the hub heights for the two cases using the following equation:  
\[k=\frac{3}{2}\Big{(}TIU_{ref}\Big{)}^{2} \tag{17}\]  
where \(U_{ref}\) the reference velocity at hub height \(H_{ref}\).  
Figure 6: Turbulence kinetic energy k (m\({}^{2}\)/s\({}^{2}\)) at hub height against the ambient turbulence kinetic energy at \(TI=8\%\).  
Figure 7: Turbulence kinetic energy k (m\({}^{2}\)/s\({}^{2}\)) at hub height against the ambient turbulence kinetic energy at \(TI=15\%\).  
The flat terrain that was chosen for the simulations diminish any additional turbulence effects of the ground at that height and benefits the wake propagation. As already mentioned above, this case aims to simulate the worst-case scenario and therefore overestimate the wake effects. By taking into account the island topography the wake effects, which express the wind farms impact to the local flow field, would be negligible. In complex terrain, with high ambient turbulence, the multiple wakes would recover faster, and any potential impact would be eliminated in a shorter distance.  
For the case of \(TI=8\%\) (Figure 5) the wake effects are observed at a maximum distance of \(5\) km, whereas for \(TI=15\%\) (Figure 6), they have already been eliminated at the same distance. The slices of Figures 5 and 6 show the additional turbulence that was produced by the wind farms. In order to qualitative compare the results, in Figures 5 and 9  
Figure 8: Velocity deficit (m/s) at hub height. (**a**) \(TI=8\%\). (**b**) \(TI=15\%\).  
Figure 9: Velocity deficit (m/s) at HUB height, projected on the complex topography of Chios island. (**a**) \(TI=8\%\). (**b**) \(TI=15\%\).  
the TKE and velocity deficit, respectively, are projected for both cases on the complex terrain of Chios using Google Earth [33].  
Following the trend of turbulence kinetic energy, the velocity deficit that was observed for the case of low turbulence intensity \(TI=8\%\) (Figures 8a and 9a), was greater against the case of \(TI=15\%\) (Figures 8b and 9b). Additionally, results confirm that in higher ambient turbulence conditions, the wake recovery is faster. This occurs from the increased mixing of the wake effects with the ambient free stream flow. For the same reason, a faster wake recovery takes place also in higher wind speeds (>8 m/s). Therefore, the choice of a reference wind speed \(U_{ref}=8\) m/s, with the current wind turbine modelling characteristics, helps the wake propagation further downstream.  
By investigating the velocity deficit and the turbulence kinetic energy downstream the wind farms it is clear that for the current layout, any impact will be eliminated after 10 rotor diameters downstream, even at the non-realistic worst-case scenario of low turbulence intensity. Figures 5 and 9 aim also to present the local complexity and increased roughness of the ground which in practice is expected to increase the vertical mixing of the flow and therefore reduce further the wake effects downstream.