Roughness Model for Unresolved Sub-grid Structures in Turbulent Flow Over Fractal Urban-like Topographies*

Turbulent flows over multiscale, fractal-like topographies are investigated via large-eddy simulation (LES). Iterated function system (IFS) topographies were used to construct urban-like, fractal geometries. The IFS featured the same central square-based prism for generation one, while predefined changes to the mapping function altered the number of descendant generations and thus the fractal dimension. In this way, fractal dimension could be nominated a priori. These idealized synthetical geometries possess the salient features of real urban topographies without the confounding complexities that would otherwise inhibit general scientific deductions. Five fractal dimensions were used to investigate the parameterization of unresolved generations. We quantified the momentum deficit associated with changing attributes, which enabled a posteriori deduction of roughness length parameters needed to model aerodynamic surface stress. We further showed that the aerodynamic stress associated with descendant, sub-generation elements can be parameterized, with only the first few generations resolved on the computational mesh.