This research will be conducted collaboratively at Clemson University, the Pennsylvania State University, and the National Center for Atmospheric Research. It focuses on issues met in using large-eddy simulation (LES) to predict the statistics of the atmospheric boundary layer (ABL). LES has become an effective research tool for the ABL and probably the most important simulation method for it. In LES, processes occurring on scales too small to be resolved by the numerical grid are diagnosed based on larger scale processes that can be resolved by the grid, using a subgrid-scale (SGS) model. However, near the ground, in the atmospheric surface layer, LES suffers from inherent under-resolution and poor SGS model performance. An integrated research program will be conducted consisting of field measurements and numerical simulations to improve SGS model performance. This research investigates the impact of the SGS turbulence on the resolvable-scale statistics in the surface layer by using field measurements to analyze the transport equations of SGS stress and flux, and the transport equation of the joint probability density function (JPDF) of resolvable-scale velocity and scalars. The field program will employ the array technique developed during prior NSF-supported research to measure the resolvable- and subgrid-scale variables. It will, for the first time, include measurements of the advection of the SGS stress and flux, which is essential for studying the SGS dynamics and for evaluating the new SGS models. The observations will be further analyzed by obtaining modeled SGS stress and flux using LES fields as model inputs to compute the SGS variables in the JPDF equation, which then will be compared with observations. This research is expected to significantly advance the understanding of the dynamics of the SGS stress and temperature flux, and their impact on the resolvable-scale dynamics. The research has broader impacts in several areas. It will provide education and research opportunities for two graduate students. New data analyses and processing methods developed in this research will further the understanding of the potentials and limitations of the array measurement technique as an essential tool for other important boundary layer applications such as area-averaged flux measurements. Improved LES will be important for improving predictive tools for applications to air-pollution modeling, weather forecasting, and land-atmosphere interaction modeling. These improved tools will greatly benefit society.
This project aimed at improving our understanding of subfilter-scale modeling for large eddy simulation of flows in the atmospheric boundary layer. Another major objective was the understanding of processes within the atmospheric surface layer (lowest portion of the atmospheric boundary layer), with particular attention to the Monin-Obukhov Similarity Theory, which is the main framework for interpreting experimental data in the atmospheric surface layer and it is employed when coupling land or oceanic fluxes to the atmospheric state in virtually all climate, oceanic, regional atmospheric, hydrological and ecological models. Three main areas of research were developed at Penn State as part of the activities funded by this project: (i) study of subfilter-scale modeling using transport equations, (ii) development of new models to predict the subfilter-scale portion of the turbulent kinetic energy, and (iii) a study of random errors and its consequence for Monin-Obukhov Similarity Theory. In addition, a major field campaign (AHATS - Advection Horizontal Array Turbulence Study) was carried out as part of this research. The main outcomes of the present research are listed below: 1) We developed better understanding of the use of transport equations to model subfilter-scale fluxes in large eddy simulation. Characterization of the improvements obtained by including the transport equations were demonstrated and the increased computational cost was quantified. Overall, the use of this approach leads to more realistic predictions of turbulence statistics when simulation results are compared to field experimental data. 2) We developed a new model for the subfilter-scale component of the turbulent kinetic energy that is applicable to atmospheric boundary-layer flows. This model was shown to produce good results in a priori studies using experimental data. 3) We developed a new technique to estimate random errors in turbulence statistics. The major advantage of the new technique is that it does not require an estimate of the integral scale of the statistic being estimated. It is well known that estimating integral scales from measurements in the atmospheric boundary layer is difficult. The proposed technique has been demonstrated to work well for the AHATS data. 4) We developed a set of equations to propagate random errors from turbulence moments to Monin-Obukhov variables and functions. This lead to the first estimate of random errors in plots of the similarity functions. Rigorous statistical analysis yielded a striking result: the scatter of data points typically observed in plots of the similarity functions is not completely explained by random error, and may be caused by missing physics in the theory itself. We have also shown that in unstable conditions, it is difficult to accurately determine the value of z/L due to excessive random errors. This result implies that we can certainly recognize unstable periods, but is it hard to quantify how unstable a given period actually is. 5) We have also developed a new theory to determine the similarity function for the mean shear from characterization of the turbulence alone. We observe from data analysis that the stability dependence of the three physical processes – the integral length-scale of turbulence, the anisotropy of the large scale eddies, and local TKE imbalance – explain most of the changes in the mean velocity profile with atmospheric stability. 6) So far a total of 6 journal papers were produced and a number of presentations were given in conferences by the principal investigators and graduate students involved.
