4.2.3. DMD Analysis

Figure 7 depicts the DMD amplitude spectra and the most dominants modes. Figure 7a shows the spectrum computed by the AD model with three distinct peaks remarked. As seen, the Strouhal number of the first peak (*φ*1) is 0.17, which falls in the range of the bluff body vortex shedding frequencies. This dominant mode, illustrated by Figure 7b, shows that the transversal velocity in the wake alters the direction regularly in a way resembling to the wake behind a circular cylinder [43]. The other two modes of the AS illustrated in Figure 7c,d are at higher frequency. The spatial scale of the oscillation decreases as the Strouhal number increases. These two modes have larger amplitudes on the wake boundary than in the wake center. For the second mode *φ*2, stronger velocity amplitude is observed in the far wake, whereas *φ*<sup>3</sup> shows a local concentration of energy in 2*D* < *x* < 6*D*.

On the other hand, the spectrum of the AS case (Figure 7e) shows a dominant peak close to the bluff body vortex shedding frequency at *St* = 0.23, which is the second larger peak in the DMD spectrum with the largest mode at *St* = 0.08. The first mode of the AS case (wavelength ≈ 9*D*) is significantly larger as shown in Figure 7f. The second mode from the AS case (Figure 7g), on the other hand, is close to the first mode from the AD case, although the wavelength of *φ*<sup>2</sup> from the AS case is smaller. Moreover, it is observed that the spectrum from the AS case has larger energy at the low frequency range than that of the AD. The two modes of higher frequency (*φ*<sup>2</sup> and *φ*3) computed from the AS model are both stronger in the far wake than in the near wake with both larger spatial scales when compared with the AD case.

It is also worth noting that the influence of the nacelle on the far wake is less evident compared to the uniform inflow case, that two (the AS case) or three (the AD case) dominant DMD modes are obviously related to the nacelle for the uniform inflow cases, while only the third dominant mode from the AS case (Figure 7h) seems to be magnified by the nacelle for the turbulent inflow cases. Detailed space-time correlation study [44] is needed to further examine the effect of nacelle on wake dynamics under turbulent inflows.

**Figure 7.** Turbulent inflow: Dynamic mode decomposition (DMD) analysis of the velocity field on the horizontal plane at the hub height (*z* = *z*hub). (**a**,**e**) the eigenvalue-weighted amplitudes of the DMD modes for the AD and the AS models; (**b**–**d**) the largest three DMD modes ordered by Strouhal number of AD; (**f**–**h**) the largest three DMD modes ordered by Strouhal number of AS. DMD modes are shown with the spanwise velocity contour.
