Turbulent flow fields over topographies are important in the area of wind energy. The roughness, slope, and shape of a hill are important parameters affecting the flow fields over topographies. However, these effects are always examined separately. The systematic investigations of these effects are limited, the coupling between these effects is still unrevealed, and the turbulence structures as a function of these effects are still unclear. Therefore, in the present study, the flow fields over twelve simplified isolated hills with different roughness conditions, slopes, and hill shapes are examined using large eddy simulations. The mean velocities, velocity fluctuations, fractional speed-up ratios, and visualizations of the turbulent flow fields are presented. It is found that as the hill slope increases, the roughness effects become weaker, and the roughness effects will further weaken as the hill changes from 3D to 2D. In addition, the fractional speed-up ratio at the summit of rough hills can even reach to three times as large as that over the corresponding smooth hills. Furthermore, the underestimation of the ratios of spanwise fluctuation to the streamwise fluctuation by International Electrotechnical Commission (IEC) 61400-1 is quite obvious when the hill shape is 3D. Finally, coherent turbulence structures can be identified for smooth hills, and as the hill slope increases, the coherent turbulence structures will experience clear evolutions. After introducing the ground roughness, the coherent turbulence structures break into small eddies.

The flow fields over a simplified 3D hill covered by vegetation have been examined by many researchers. However, there is scarce research giving the three-dimensional characteristics of the flow fields over a rough 3D hill. In this study, large eddy simulations were performed to examine the coherent turbulence structures of the flow fields over a vegetation-covered 3D hill. The numerical simulations were validated by the comparison with the wind-tunnel experiments. Besides, the flow fields were systematically investigated, including the examinations of the mean velocities and root means square of the fluctuating velocities. The distributions of the parameters are shown in a three-dimensional way, i.e., plotting the parameters on a series of spanwise slices. Some noteworthy three-dimensional features were found, and the mechanisms were further revealed by assessing the turbulence kinetic energy budget and the spectrum energy. Subsequently, the instantaneous flow fields were illustrated, from which the coherent turbulence structures were clearly identified. Ejection-sweep motion was intensified just behind the hill crest, leading to a spanwise rotation. A group of vertical rotations were generated by the shedding of the vortex from the lateral sides of the hill.