Large-eddy simulation of turbulent boundary layer over sinusoidal hills and multiscale complex topography.

University of Minnesota Ph.D. dissertation. August 2011. Major:Civil engineering. Advisor: Fernando Port´e-Agel. 1 computer file (PDF); viii, 83 pages.Atmospheric models require the parameterization of surface fluxes at regional scales. The accuracy of the parameterization relies on detailed information on the spatial and temporal distribution of turbulence in the atmospheric boundary layer (ABL). Large-eddy simulation (LES) has become an increasingly popular tool to study the ABL and obtain the three-dimensional transient information of the ABL. It uses a subgrid-scale (SGS) model to parameterize the subgrid turbulent transport. Here, three different SGS models are tested in LES of neutrally as well as stably stratified boundary layers over rough two-dimensional sinusoidal hills. The examined SGS models include the standard Smagorinsky model with a wall-matching function, the Lagrangian dynamic model, and the recently developed scale-dependent Lagrangian dynamic model. Simulation results obtained with different models are compared with turbulence statistics from wind tunnel experiments. We find that the scale-dependent Lagrangian dynamic model is able to dynamically (without any parameter tuning) capture the scale dependence of the model coefficient associated with regions of the flow with strong shear and/or thermal stratification. This scale-dependent dynamic procedure substantially improves the simulation results with respect to both the standard (non-dynamic) eddy-viscosity/diffusivity model and the scale-invariant dynamic model. LES with the tested scale-dependent Lagrangian dynamic model is used to study neutral ABL flow over multiscale complex topography, which is generated using the restricted solid-on-solid (RSOS) model and able to capture the power-law scaling property of a -2 slope of elevation power spectrum in a log-log scale found in many natural landscapes. The parameterization needed to represent the effect of SGS topography in numerical models (e.g., coarser LESs or high-resolution weather models) of ABL flow is investigated. Specifically, the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography is proposed. Results from LESs performed using elevation fields pass-filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevation, and support the proposed formula. High-resolution multiscale topography may not be directly represented in a LES of the ABL. One needs to spatially filter it to obtain a resolved topography to be directly used in LES and a SGS topography whose effect on the ABL needs to be parameterized. Here we propose a parameterization scheme of using a SGS roughness length in the lower boundary condition (the logarithmic law under neutral condition) in LES. The formulation of the SGS roughness length is proposed. The validity of the parameterization scheme is examined by simulating neutral ABL flow over a series of complex terrains that are filtered from a high-resolution multiscale topography at varying scales. Without applying the parameterization scheme in the series of simulations, the area-averaged velocity profiles over the series of terrains show clear discrepancies. After considering the parameterization of SGS topographic effect, that is, applying a SGS roughness length in the surface boundary condition, the velocity profiles show clear convergence and the validity of the parameterization scheme is proved