A priori testing and development of subgrid-scale models for Large Eddy Simulation of the atmospheric boundary layer

J. Kleissl
PhD Thesis, The Johns Hopkins University
February 2004
Baltimore MD

ABSTRACT: Large-eddy simulation (LES) has become an indispensable tool for prediction of turbulent atmospheric boundary layer (ABL) flow. In LES, a subgrid-scale (SGS) model accounts for the dynamics of the unresolved scales of motion. The most widely used SGS model is an eddy viscosity closure, the Smagorinsky model, which includes a parameter that must be prescribed in some fashion, the Smagorinsky constant cs. In this dissertation, cs is measured in a specifically designed field experiment. And, the ability of so called dynamic SGS models to predict $c_s$ is studied based on the data obtained, as well as in numerical simulations.

In the field study, two vertically separated horizontal arrays of 3d-sonic anemometers are placed in the atmospheric surface layer. Results indicate that cs is reduced when the integral scale of turbulence is small compared to the grid or filter scale, such as near the ground and in stable atmospheric conditions. The field data are processed further to test whether dynamic SGS models can predict the correct coefficient values. In the scale-invariant dynamic model (Germano et al. 1991), the coefficient is derived from various data test-filtered at a larger scale assuming that cs is the same as at scale D. The results show that cs is significantly underpredicted whenever D is larger than the large-scale limit of the inertial range. The scale-dependent dynamic model (Porté-Agel et al. 2000b) uses a second test-filter to deduce the dependence of cs on filtering scale. This model provides excellent predictions of cs its dependence upon stability and height.

Large eddy simulations of flow over a homogeneous surface with a diurnal heat flux forcing are conducted to study the prediction of $c_s$ over a wide range of stabilities in a numerical framework. The scale-invariant and scale-dependent Lagrangian dynamic SGS model are tested and compared to the field data. Consistent with the field studies, the prediction of cs from the scale-invariant model is too small, whereas the scale-dependent coefficients are more realistic. The simulation also yields new results: cs exhibits hysteresis behavior in the mixed layer. It is found that in unstable conditions, neither a surface layer parameter (Obukhov length) nor other stability parameters (gradient Richardson number) could uniquely characterize cs there. Thus, we conclude that the dynamic model, which does not require such ad-hoc characterizations, is an attractive parameterization strategy for LES of ABL.