## 3 Results
### Influence of the Atmospheric Stability on Wind Speed Gradients
#### 3.7.2 Interaction of Coastal Wind Speed Gradients with OWF Wakes  
The OWF wakes are characterised by a deceleration of wind speed downwind from the wind farms. The length of the wakes depends on stability, where thermally stable boundary layers are favorable for longer wakes, while unstable stratification tends to diffuse wakes relatively quickly due to higher vertical momentum fluxes [16; 17; 38; 50; 53]. In the following we will have a closer look at the interaction of coastal effects with atmospheric wakes generated by the cluster N-4. Figure 14a,b show the horizontal wind speed gradients for the class \"INCS\" that are associated with the thermally unstable stratification for the transects \"Ref\" and \"N4\" from easterly (a) and southerly (b) winds. The associated stability transects are superimposed as green curves with separate vertical axis on the right. The SAR measurements within the OWFs are contaminated by the strong radar reflection from wind turbines and are therefore not used for wind speed estimation. For both wind directions, as expected, the \"Ref\" cases presents continuous curves, with a rapid increase in the first 50 km followed by a nearly steady state. It is obvious that for easterly wind directions the cluster N-4 is located in an area with significant lateral wind speed gradients associated with coastal effects. For southerly wind directions the spatial variability of the background wind field within cluster N-4 is smaller because the upstream distance to the coast is longer and wind speeds are closer to equilibrium. Before impinging the cluster N-4, the \"Ref\" and \"N4\" relatively display comparable horizontal wind speed gradients. The main differences arise downstream of the wind farm with roughly 5% smaller wind speeds in the transect passing through the OWF. In easterly winds the wind speed downstream of the OWF is actually higher than upstream. This means that the impact of the wakes on the wind is more than compensated by the coastal effect. However, a slight negative slope or gap between the upstream and downstream wind amplitude that depicts wind deficit can be seen in the first 15 km after crossing the cluster N-4 for the southerly wind. This indicates wake impacts are still present in the downstream wind field. Overall, the horizontal wind speed gradients for \"N4\" show an increasingly weak slope downstream the wind farm in comparison to \begin{table}
\begin{tabular}{c c c c c c} \hline
**Atmospheric** & \(\Delta\mathbf{u}\) & \(\mathbf{x_{95\%}}\) & \(\mathbf{R^{f}}_{max}\) & \(\mathbf{u_{land}}\) & \(\mathbf{u_{offshore}}\) \\
**Stability** & **(m/s)** & **(km)** & **(\%)** & **(m/s)** & **(m/s)** \\ \hline \multicolumn{6}{c}{_Easterly wind_} \\ \hline Unstable & 3.2 & 72 & 37 & 8.6 & 11.9 \\ Stable & 2.8 & 115 & 78 & 3.7 & 6.5 \\ \hline \multicolumn{6}{c}{_Southerly wind_} \\ \hline Unstable & 2.3 & 30 & 31 & 7.5 & 9.8 \\ Stable & 2.4 & 50 & 43 & 5.4 & 7.8 \\ \hline \end{tabular}
\end{table} 
Table 3: Recap of estimated parameters \(\Delta u\), \(x_{95\%}\), \(u_{offshore}\), \(u_{land}\), \(R^{f}_{max}\) from the empirical model for stable and unstable conditions for easterly and southerly unperturbed winds. the \"Ref\" cases. The normalised wind speed increase (not shown) is lower for \"N4\" than for \"Ref\" for both wind directions. In Figure 14c,d, \(u_{10}\) for the class \"INCS\" related to stable stratification are considered. Upstream the wind farm, the wind speed amplitude from \"Ref\" is lower than \"N4\" for easterly winds (Figure 14c), while the wind field from \"Ref\" and \"N4\" are quite similar for southerly winds (Figure 14d). Overall, for easterly and southerly winds, the curves of \(u_{10}\) from \"N4\" display a significant drop in wind amplitude immediately downstream the cluster N-4, which extends at least over 20-30 km. This wind speed decrease reflects the wake effects that have superimposed the background air flow.