  High-fidelity large-eddy simulations are suitable to obtain insight into the
complex flow dynamics in extended wind farms. In order to better understand
these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and
reconstruct the flow field in large-scale numerically simulated wind farms by
large-eddy simulations (LES). Different wind farm layouts are considered, and
we find that a combination of horizontal and vertical staggering leads to
improved wind farm performance compared to traditional horizontal staggering.
We analyze the wind farm flows using the amplitude selection (AP) and
sparsity-promoting (SP method) DMD approach. We find 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 find that a relatively limited number of SP-DMD modes is sufficient
to accurately reconstruct the flow field 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 flow field.
