Turbulent wake dynamics and flow characteristics over typical hilly terrain: A proper orthogonal decomposition and dynamic mode decomposition analysis

The turbulent wake dynamics over hilly terrain with typical topographic shapes and slopes under different oncoming flow conditions are numerically investigated using large-eddy simulations, followed by proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) analysis. First, the effects of terrain shape, slope and inflow turbulence on the statistical and spectral characteristics of wake turbulence over hilly terrain are clarified. Then, the dominant flow patterns in the topographic wake are identified by POD and DMD, respectively. Finally, the turbulent wake flow fields over typical hilly terrain are reconstructed using DMD. The results show that the peak spectral frequencies at half topography elevation decrease as the terrain shape transitions from three-dimensional to two-dimensional but increase with decreasing terrain slope and oncoming turbulence intensity. From POD and DMD analyses, it is demonstrated that the wake dynamics over steep terrain under turbulent inflow conditions are predominantly governed by the separated shear layer shed from the hillside and hilltop on the horizontal and vertical planes, respectively. Some discrepancies are observed in the higher-order modes extracted from POD and DMD, indicating strong interactions among multi-frequency eddy motions in the topographic wake. Moreover, the wake fields over typical hilly terrain under different incoming flow conditions can be effectively reconstructed using only 30% of DMD modes with reasonable accuracy. The reconstruction errors are primarily concentrated within the separated shear layer due to the strong flow nonlinearity in this region.