A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics

High- fi delity large-eddy simulations are suitable to obtain insight into the complex fl ow dynamics in extended wind farms. In order to better understand these fl ow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct the fl ow fi eld in large-scale numerically simulated wind farms by large-eddy simulations (LES). Different wind farm layouts are considered, and we fi nd that a combination of horizontal and vertical staggering leads to improved wind farm performance compared to traditional horizontal staggering. We analyze the wind farm fl ows using the amplitude selection (AP) and sparsity-promoting (SP method) DMD approach. We fi nd that the AP method tends to select modes with a small length scale and a high frequency, while the SP method selects large coherent structures with low frequency. The latter are somewhat reminiscent of modes obtained using proper orthogonal decomposition (POD). We fi nd that a relatively limited number of SP-DMD modes is suf fi cient to accurately reconstruct the fl ow fi eld in the entire wind farm, whereas the AP-DMD method requires more modes to achieve an accurate reconstruction. Thus, the SP-DMD method has a smaller performance loss compared to the AP-DMD method in terms of the reconstruction of the fl ow fi eld. © Elsevier Ltd. rights reserved.