Abstract 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.

中文翻译：

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坡度对孤立山脊流场影响的大涡模拟

摘要 山坡的坡度会显着影响流型。在本研究中，三个光滑的三维 (3D) 山丘 (H2、H4 和 H8) 和三个光滑的二维 (2D) 山脊（R2、R4 和 R8），山丘高度增加了 2.0 倍，而山半径保持恒定以实现不同的坡度，使用大涡模拟 (LES) 进行系统检查。随着坡度的增加或形状从 3D 山丘变为 2D 山脊，水流的重新附着变得困难。此外，随着坡度的增加，3D山丘和2D山脊之间的流场差异将变得更加明显。此外，H2 和 R2 的平均速度和波动几乎相同，而随着山坡的增加，3D 山和 2D 山脊之间的差异变得越来越大，对于 H8 和 R8，3D 山丘和 2D 山脊之间的相似性几乎消失了。基于从 LES 获得的信息，提出了一种预测分数加速比的分析模型。对于 3D 山丘上的湍流结构，识别出螺旋结构，螺旋的螺距随着山坡坡度的增加而变窄。当山坡进一步增加到H8时，螺旋结构被破碎成分离的圆管。对于R4，确定了发夹结构，而对于R8，发夹结构消失了，并且周期性地出现了具有长展向尺寸的涡流。对于 3D 山丘上的湍流结构，识别出螺旋结构，螺旋的螺距随着山坡坡度的增加而变窄。当山坡进一步增加到H8时，螺旋结构被破碎成分离的圆管。对于R4，确定了发夹结构，而对于R8，发夹结构消失了，并且周期性地出现了具有长展向尺寸的涡流。对于 3D 山丘上的湍流结构，识别出螺旋结构，螺旋的螺距随着山坡坡度的增加而变窄。当山坡进一步增加到H8时，螺旋结构被破碎成分离的圆管。对于R4，确定了发夹结构，而对于R8，发夹结构消失了，并且周期性地出现了具有长展向尺寸的涡流。