Dynamic mode decomposition and mechanism analysis of unsteady wind turbine wake evolution in complex terrain

As wind energy shifts to complex terrains, the unsteady evolution of turbine wakes—marked by three-dimensional inhomogeneity and low-frequency unsteadiness—poses challenges for power optimization and structural integrity. This study develops a robust reduced-order model integrating large eddy simulation and dynamic mode decomposition (DMD) to decode wake-topography interactions. Findings show the I-criterion offers superior interpretability over the traditional α-criterion. By accounting for spatiotemporal persistence, it captures critical low-frequency instability modes governing far-field meandering while filtering high-frequency transients. The research elucidates key “topography-wake” coupling mechanisms: favorable pressure gradients on windward slopes elongate wake structures, while adverse gradients at hilltops trigger multiscale structural nesting and accelerated energy cascades. Downstream, intense turbulence exerts a “decoupling effect,” fragmenting coherent topologies. For the idealized two-dimensional Gaussian-hill and neutral-atmospheric boundary layer cases considered here, retaining 30% of the dominant modes keeps the reconstruction error below 10% while preserving the main wake topology and meandering phase information. These results demonstrate the feasibility of DMD-based reduced-order analysis for idealized terrain-modulated wakes and provide a basis for future extension to more realistic three-dimensional terrains and atmospheric conditions.