Wall Modeling for Turbulent Flow over Complex Roughness
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Turbulent flow over complex rough surfaces is crucial in both engineering and boundary layer meteorology science. The surface morphology has significant effects on the flow, but it is computationally expensive to solve all the turbulent scales especially when the air flows over complex roughness. Large-eddy simulation (LES) with wall model is therefore employed in this situation. This dissertation focuses on the wall modeling of turbulent flow over complex roughness such as urban topography. As the wall effects can be accurately represented by the equilibrium logarithmic law via roughness length, z0, this dissertation aims to parameterize z0 over complex roughness. In this dissertation, two types of complex roughness are discussed: spatially heterogenous urban-like topography (Chapter 3) and multiscale fractal urban-like topography (Chapter 4). For the spatially heterogeneous urban-like topography, a priori prediction method for z0 based on the statistical moments of surface height is proposed especially for the boundarylayer turbulent flow. Using a posteriori LES results, we demonstrate that the skewness of surface height (as measures of the presence of the extreme value, or the “heavy tail” events) has non-negligible effects, which received less attention as topographic parameters in the past. This finding is reconciled with a model recently proposed by Flack and Schultz (2010) who demonstrate that z0 can be modeled with standard deviation and skewness, and two empirical coefficients (one for each moment). We find that the empirical coefficient related to skewness is not constant but exhibits a dependence on standard deviation over certain ranges. For idealized, quasi-uniform cubic topographies and complex, fully random urbanlike topographies, we demonstrate robust performance of the generalized Flack and Schultz model against contemporary roughness correlations. The multiscale fractal-like topographies pose a particular challenge to numerical simulation schemes since the large-scale elements are resolved, but the small-scale descendant elements cannot be resolved on the computational mesh grid. A local wall model representing the effects of unresolved sub-generation roughness is needed in such scenario. By virtue of selfsimilarity among scales, we develop a methodology and a roughness model for the unresolved scales by learning from the large-scale momentum fluxes. And then the roughness model for the unresolved scales via the equilibrium logarithmic law is established. The research shows that aerodynamic stress associated with descendant, sub-generation scale elements can be parameterized, thus that the turbulent flow over fractal-like geometry can be simulated with only the large generations resolved on the computational mesh grid. The key questions we ask in this dissertation are: How does the spatial heterogeneity affect the transport of the turbulent flow? How to model the sub-generation scales which are smaller than the mesh grid for a fractal topography? The results, and the modeling framework developed herein, have practical implications for the operation of numerical weather prediction models and the initialization of high-resolution solutions.