Large-Eddy Simulation Study of Turbulent Flow over Urban-like Fractals

Multiscale, fractal-like topographies represent a special challenge to numerical simulation schemes since the large-scale elements are resolved but the descendent small-scale elements cannot be resolved on the computational mesh. A local roughness model representing the effects of unresolved roughness is needed in such scenarios, especially given the turbulence over fractal-like geometries exhibited by Earth’s surface. Our goal is to develop a methodology and then a roughness model for the unresolved scales by learning form the large-scale fluxes. In the current research, analysis is performed by using 3-dimensional, inertial-dominated, large-eddy simulations (LES) of flow over fractal-like urban topographies. Here the fractal-like topographies were built by the iterated function system (IFS), which featured the same central square-based prism for generation one, while predefined changes to the mapping function altered descendant generations, Ng, and thus fractal dimension, D. These idealized synthetical geometries possess the salient features of real topographies without the confounding complexities that would otherwise inhibit broader scientific deductions. Five fractal dimensions over the range, 1<D<2, were used in the current research. For each fractal dimension, we modeled 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 deficit associated with changing D and Ng, which enabled a posteriori deduction of roughness length parameters needed to model aerodynamic surface stress via the equilibrium logarithmic law. In addition, results from a posteriori test, in which the effective velocity profile from parameterized models, are compared to the results from full simulations for a set of fractal geometries. The current research shows that aerodynamic stress associated with descendant, sub-generation scale elements can be parameterized, thus that the turbulent flow over fractal-like topography can be simulated with only the first few generations resolved on the computational mesh. These results, and the modeling framework developed herein, have practical implications for operation numerical weather prediction and for initialized high resolution solutions.