Large eddy simulations of slope effects on flow fields over isolated hills and ridges

The slope of a hill could affect the flow patterns significantly. In the present study, three smooth three dimensional (3D) hills (H2, H4, and H8) and three smooth two dimensional (2D) ridges (R2, R4, and R8), with the hill heights increased by factors of 2.0 while the hill radii are kept constant to achieve different slopes, are examined systematically using large eddy simulations (LES). The reattachment of the flow is found to become difficult as the slope increases or as the shape changes from 3D hill to 2D ridge. In addition, the differences of the flow fields between the 3D hills and the 2D ridges will become more evident as the slope increases. Moreover, the mean velocities and the fluctuations for H2 and R2 are almost the same, whereas as the hill slope increases, the differences between the 3D hills and 2D ridges become stronger, and the similarities between the 3D hills and 2D ridges almost disappear for H8 and R8. Based on information available from LES, an analytical model to predict the fractional speed-up ratio is proposed. As for the turbulence structures over the 3D hills, a spiral structure is identified, and the pitch of the spiral becomes narrow as the hill slope increases. When the hill slope further increases to H8, the spiral structures are broken into separated circular tubes. For R4, a hairpin structure is identified, whereas for R8, the hairpin structure disappears, and a vortex with a long spanwise size occurs periodically.