POD analysis of spatiotemporal characteristics of wake turbulence over hilly terrain and their relationship to hill slope, hill shape and inflow turbulence

In this study, the turbulent wake flow fields over isolated 2-D ridges and 3-D hills with different slopes and oncoming flow conditions are predicted by large-eddy simulations (LES). The coupling effects of hill slopes, hill shapes and inflow turbulence on the spatiotemporal characteristics of wake turbulence over hilly terrain are clarified in terms of turbulent statistics and unsteady flow patterns. The snapshot-based proper orthogonal decomposition (POD) technique is then adopted to elucidate the physical meaning of wake turbulence over hilly terrain. The numerical results show that the vertical distributions of turbulent statistics and the unsteady flow patterns in the wake of hilly terrain are jointly determined by hill slopes, hill shapes and oncoming flow conditions. Additionally, the snapshot-based POD method is capable of reconstructing a large amount of fluctuating kinetic energy in the wake of hilly terrain with a few low-order POD modes. Moreover, the primary wake patterns and their relations to hill slopes, hill shapes and oncoming flow conditions are identified. On the horizontal plane, the wake turbulence structures of 3-D gentle/steep hill are dominated by the asymmetric elongated streak structures and a pair of counter-rotating vortices, respectively. On the vertical plane, the main patterns of hill wake are often featured by the recirculating flow, and the size of recirculation bubble is highly dependent on hill slopes and hill shapes.