# Dynamic Aeroelastic Response of Stall-Controlled Wind Turbine Rotors in Turbulent Wind Conditions
## 4 Energy-Transfer Characterization of the Pulse (Stable Oscillatory Regime)
This subrange shows a much richer combination of the five frequencies observed, with three of them being dominant. Even though the 4.2 and 5.14 Hz components take a long time to decay, they are still not dominant. As before, the 0.87 Hz frequency is the most prominent, but the relative contribution of the 1.2 Hz component increases even more compared with the previous subranges. The most remarkable feature of this subrange is the emergence of a third dominant frequency of 2.4 Hz, which is particularly intense at 11 m/s. The 2.4 Hz frequency is only observed as a dominant component in this subrange specifically. Figure 8: (**a**) Time evolution of the axial displacement of the blade at a wind-speed regime of 16 m/s for pulses that combine different values of amplitude and time span. (**b**) The same curves normalized by the kinetic energy content of their respective pulses. Figure 9: Frequency spectra for the first subrange along the stable regime. (**a**) Complete time evolution. (**b**) Long-term evolution. Figure 10: Frequency spectra for the second subrange along the stable regime. (a) Complete time evolution. (b) Long-term evolution. Figure 12 shows the spectra for the fourth and last subrange, which extends from 13 to 16 m/s, where the contribution is again mostly centered around the 0.87 Hz frequency, with a stronger presence of the 1.2 Hz component. An important distinctive feature is the presence of the 0.87 Hz frequency in the long-term spectra, which indicates a longer persistence (thus, a lower exponential decay) for this component. This ever-lower exponential decay of the 0.87 Hz component leads to the end of the stable regime, where the exponential decay approaches zero and then becomes negative. Thus, the aerodynamic damping turns into exponential expansion. In this subrange, the contributions of the other three frequencies become minimal. Figure 11: Frequency spectra for the third subrange along the stable regime. (**a**) Complete time evolution. (**b**) Long-term evolution. Figure 14 shows the variation of the exponential decay of the aerodynamic damping for the complete range of wind speeds in the stable oscillatory regime. The exponential decay associated with the 0.87 Hz frequency (\(\lambda_{1}\)) shows a clear connection with the four different subranges associated with the frequency content that we have seen before. Figure 14: Variation of the exponential decay of the aerodynamic damping for the complete range of wind speeds in the stable oscillatory regime. Figure 6:0 Semi-log plots of the time evolution of the normalized blade deflection at selected wind speeds in different subranges of the stable regime. The red and blue lines indicate the enveloping curves for the decaying components of the signal associated with the first (0.88 Hz) and second (1.2 Hz) frequencies respectively. The 1.2 Hz frequency shows an exponential decay that is much lower. Even though it has a lower amplitude in the mix of frequencies, it persists for a longer time, and that is the reason for why it is more prominent in the long-term spectra. The 2.4 Hz frequency only appears in the third subrange, and it shows a sudden decrease in its exponential decay located at 11 m/s, which makes that component persist for a longer time. It returns to a higher dissipation rate at wind speeds of 12 m/s.