Turbulent flow over urban-like fractals: prognostic roughness model for unresolved generations

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, $N_g$, 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, $1\le D\le 2$, 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 $N_g$, 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.

KEYWORDS:

• Fractal
• urban micrometeorology
• atmospheric boundary layer
• turbulence

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Army Research Office, Atmospheric Chemistry Program, Grant # W911NF-15-1-0231. Computer resources were provided by the Texas Advanced Computing Center at the University of Texas at Austin, and by the Office of Information Technology at the University of Texas at Dallas.