ABSTRACT Large-eddy simulation (LES) has been used to model turbulent channel flow over urban-like, fractal topographies, constructed via iterated function system (IFS). By using the IFS approach, the topography fractal dimension, D, and a desired number of generations, , can be nominated a priori. The topographies considered herein all featured the same central square-based block for generation one, while predefined changes to the mapping function altered descendant generations, and thus fractal dimension. We selected five fractal dimensions over the range, , where smaller and larger values corresponded with urban environments that were less and more densely developed, respectively. For each fractal dimension, we modelled flow over topographies constructed with one to four iterations; the topographic elements were resolved during simulation with an immersed-boundary method (IBM). We quantified the momentum penalty associated with changing D and , which enabled a posteriori deduction of roughness length parameters needed to model aerodynamic surface stress via the equilibrium logarithmic law. We showed that aerodynamic stress associated with the descendant, sub-generation elements can be parameterised, with only the first few generations resolved on the computational mesh. Finally, a logarithmic law-based roughness model was proposed for the unresolved, sub-generation topographic elements. Additional testing revealed that turbulence statistics (to the third-order) responded most dramatically to the first generation – in this case, a large central block – while the turbulence statistics are relatively similar whether the effects of additional generations are resolved or modelled.

中文翻译：

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城市分形上的湍流：未解决世代的预测粗糙度模型

摘要 大涡模拟 (LES) 已被用于模拟通过迭代函数系统 (IFS) 构建的类似城市的分形地形上的湍流通道流动。通过使用 IFS 方法，可以先验地指定地形分形维数 D 和所需的代数 。这里考虑的地形都以第一代相同的基于中心正方形的块为特征，而对映射函数的预定义更改改变了后代，从而改变了分形维数。我们在 范围内选择了五个分形维数，其中较小和较大的值分别对应于较不发达和较密集的城市环境。对于每个分形维数，我们对通过一到四次迭代构建的地形流进行建模；在模拟过程中使用浸入边界方法 (IBM) 解析了地形元素。我们量化了与改变 D 和 相关的动量损失，这使得能够通过平衡对数定律对模拟空气动力学表面应力所需的粗糙度长度参数进行后验推论。我们展示了与后代、子代元素相关的空气动力应力可以参数化，只有前几代在计算网格上解析。最后，针对未解析的子代地形元素提出了基于对数定律的粗糙度模型。额外的测试表明，湍流统计（三阶）对第一代反应最显着——在这种情况下，