Flow and transport processes in the atmosphere are strongly influenced by orography that generates forces and causes complex flow distortions. At smaller scales, the atmospheric surface layer is also affected substantially by vegetation canopies. Most previous work has focused on effects of hills and vegetated terrain characterized by a single length scale, e.g. a single hill of a particular size, or canopies consisting of plants, often modeled using a prescribed leaf-area density distribution. It is well known, however, that flow obstructions such as mountain ranges and canopies are characterized by a wide range of length scales. Yet, it is not known how to parameterize the effects of such multi-scale objects on the lower atmospheric dynamics. This research addresses this issue with an integrated laboratory experimental and computational program, focusing on atmospheric boundary layer flow over fractal shapes. Fractals provide convenient idealizations of the inherently multi-scale character of mountain range and vegetation geometries, within certain ranges of scales. The experiments consist of laboratory model studies of flow structure and drag forces in an "optically index-matched" facility, where unobstructed, detailed flow and force measurements can be performed within the entire complex domain. Multi-plane particle image velocimetry measurements will provide all components of the stress and velocity gradient tensors. A key motivation for the experimental work is the need to validate and support further development and improvements of a new prediction tool, Renormalized Numerical Simulation (RNS). This technique models forces from unresolved features of the ground topology using drag coefficients determined from interrogation of the large scales that are explicitly resolved on the computational mesh, followed by dynamic rescaling. The RNS will be used to model the flow across fractal trees and mountain ranges, and compare the predicted forces and flow features with the measurements. With the detailed flow data available, causes for discrepancies will be identified and used for improvements.
Research on improving scientific foundations of sub-grid parameterizations of land-atmosphere interactions, the subject of the project, has a broad impact on the infrastructure of atmospheric and climate sciences. Measurements using novel, optically index-matched, methods in the context of atmospheric flow phenomena provide the possibility of a quantum step in the level of detail with which flows can be mapped and understood. Moreover, the development of properly validated RNS applied to flow with fractal boundaries may yield broader impact in areas other than turbulent boundary layers over multi-scale ground topology. Fractals have been used as a descriptive tool in many disciplines, such as biology (branching blood network, pulmonary structures, corals), astrophysics (large-scale structure of the universe, intermittency of interplanetary magnetic fields), and other geosciences aspects (fractal coastlines, clouds). RNS extends the geometric idea of fractals to fluid dynamics. Educational impact of the work will focus on graduate education/training that stresses the interplay between physical experimentation and simulation. As part of the educational outreach effort, interactions with the Baltimore City School system will continue and strengthen. Specifically, senior high-school students from the Baltimore Polytechnic Institute will be involved in yearlong research experiences in our laboratory, as part of their required Research Practicum. Involvement in research on atmospheric flows over fractal boundaries will help motivate talented senior high-school students to consider future careers in this field.
This project aimed at improving our understanding of the exchanges and coupling between multi-scale vegetation elements and the atmospheric boundary layer. Motivating the research was the fact that typical vegetation elements contain a multiplicity of length-scales, such as branches, sub-branches, etc. Classical models rely on understanding of objects characterized by a single, or at most a few, characteristic length-scales. It was decided to study interactions of fractal-like trees with boundary layer flows, since fractal geometry can be used to efficiently characterize such shapes. Fractal trees thus provide a convenient idealization of the inherently multi-scale character of vegetation elements, within certain ranges of scales. In the present study we only focused on momentum fluxes (drag forces) for cases where the vegetation elements are all very "stiff", i.e. branches do not sway in the wind. Particle Image Velocimetry (PIV) measurements in the wake of a single fractal-like tree (see Figure 1) were analyzed in detail, and the data were used to identify the distribution of mixing length scales across the wake. The results presented several interesting trends that had not been observed before, such as decreasing length-scales with height (as suggested in Fig. 1c), but decreasing at a much slower rate (it was about a factor of two) compared to the decrease in scale associated with the tree generations, for which the ratio between the largest and smallest branch diameters was a factor 32. In order to understand the observed trends, models based on superposition of scales were developed and shown to describe the measured trends well (see Figure 2). The results demonstrated that certain transport processes between canopies containing multi-scale elements and the atmosphere can be described using a single effective length-scale, but that this effective scale must be obtained using explicit superposition and weighing of the canopy elements’ multiple length-scales. Furthermore, the data were used to evaluate the so-called subgrid-scale energy flux, which characterizes the turbulent energy cascade across scales. A related computational study focused on developing Renormalized Numerical Simulation (RNS) to model subgrid-scale drag forces in the context of Large Eddy Simulation. Variants of the technique were proposed and evaluated, and the most appropriate variant was applied to simulate a canopy of fractal trees. Figure 3 shows representative snapshots of simulated distributions of stream-wise velocities as a turbulent atmosphere interacts with a canopy of fractal trees. The results obtained from this project show that multi-scale and clustering properties of fractal objects should be incorporated when estimating characteristic length scales to describe how the object interacts with the atmospheric boundary layer processes. So far a total of 2 journal papers were produced as well as 1 conference proceedings paper, 1 journal paper in preparation, and 3 abstracts. A total of 17 talks based on this grant were presented (at AGU, EGU, APS, seminars) by the principal investigators and graduate students involved.
