## 3 Comparison Based on Numerical Simulation
### Numerical Simulation of Non-Stationary Flow Field  
To simulate flow field B, we linearly decomposed an original non-stationary wind velocity sample measured at the Pengcheng power station engineering site on 29 November 2011 into intrinsic mode functions (IMFs) with varying dominant frequencies using the empirical mode decomposition technique first [17], as depicted in Figure 3. To illustrate the energy distributions of different components obtained, FFTs are applied to these IMFs, and the results in the form of amplitude spectral densities (ASDs) are shown in Figure 4. For the spectra obtained to be less noisy and discernable, the original time-history and IMFs 1-6 (the black curves shown in Figure 3) are smoothed using the five-point FFT technique to generate the new samples for use (the red curves shown in Figure 3) before being transformed into ASDs. As can be seen in Figure 4a, among these high-frequency IMFs (IMFs 1-5), only IMF 1 possesses the commensurate energy in the high-frequency domain (5-10 Hz) compared with the original velocity sample. However, all the low-frequency IMFs (IMFs 7-12) and the residue have the same ASDs in the low-frequency domain (0.001-0.01 Hz) compared with the original velocity sample (see Figure 4b). According to ref. [17], all these low-frequency IMFs and the residue should be responsible for the non-stationarity of the original velocity sample. To reconstruct the original velocity sample, IMFs 1 and 7-12 and the residue should be employed based on the linear superposition method with respect to the energy distribution of the reconstructed sample in the full frequency domain and the non-stationary feature of the reconstructed sample. To transform the non-stationary velocity sample into a sinusoidal function, the resulting IMFs (IMFs 1, 7-12, and the residue) were then approximated using basic sinusoidal waves with different periods (see Figure 5). To illustrate this point further, we can look at the basic sinusoidal wave for IMF 11 shown in Figure 5g. The comparison of the two curves in Figure 5g demonstrates that the basic sinusoidal wave for IMF 11, which is represented by the equation \(y=0.4\sin(0.078t-20)\) (where y is the wind velocity in m/s and t is time in seconds), closely resembles IMF 11 in the time domain in terms of the period and the amplitude. Additionally, it is found that the amplitude spectral density of IMF 11 overlaps that of the basic sinusoidal wave in the frequency domain, indicating that IMF 11 and its basic sinusoidal wave possess comparable energy. The same observation can be made for the basic sinusoidal waves associated with other IMFs (see Figure 5). Table 2 lists the amplitude, the frequency, and the phase of all components. Based on the above analyses, we finally obtain a senior sinusoidal function obtained by the linear superposition of all basic sinusoidal functions shown in Figure 5, written as Equation (3). This senior sinusoidal function can well approximate the original non-stationary velocity sample measured atthe Pengcheng power station engineering site. As shown in Figure 6, the original non-stationary velocity sample and the simulated senior sinusoidal function are basically close together in both the time and frequency domains, suggesting the validity of the proposed method in simulating the non-stationary flow field. Although the evidence approximately holds for the linear superposition practice to simulate the non-stationary flow field, only one specific case is considered, and more rigorous examinations will be performed in the future in order to make the general claims about the proposed simulation method. At present, we restrict the claim to the flow around Pengcheng cooling tower in the specific wind environment. \[y=0.2\sin(62.8t)+0.2\sin(1.57t)+0.15\sin(0.785t)+0.2\sin(0.5t)+0.2\sin(0.25t)+0. 2\sin(0.126t) \tag{3}\] \[+0.4\sin(0.078t-20)+0.4\sin(0.021t)+12.5\]  
Figure 3: EMD decomposition of the wind velocity sample measured in the field.