People
| Graduate Student | Kunlun Bai |
| Project Supervisors | Prof. Charles Meneveau Prof. Joseph Katz |
| Design and Technical Support | Yury Ronzhes |
Fractal Canopy
Vegetation canopy has a significant impact on various physical and biological processes, such as the forest microclimate, rainfall evaporation distribution and climate change. In all these processes, complex flows occur within and above the vegetation canopy. Flows would affect the plant growth, affect the seed dispersal, affect the production of food, materials and energy, and so on. Based on several aspect, study of canopy flows is very important.
During last three decades, extensive studies had been conducted both in the field and lab. For lab experiments, except for some examples, most of the studies utilized objects only with one length scale. In reality, trees have multiple scales. To get a better understanding of the canopy flows, model with multiscale is needed.
In our experiments, trees with fractal features are used (see section: Fractal tree). The fractal preserves multiple scales and at the same time it can be described in simple ways. Because of its multiscale feature, the scale interactions in the flows can be explored and then a better understanding of the flows generated by multiscale objects can be obtained which may improve our understanding about canopy flows.
In our fractal canopy, the material of some trees is acrylic which has the same refractive index as the solution in the facility. Because of this unique feature of our facility, we can obtain detailed flow fields between the branches inside the tree.
We already performed the detailed PIV measurements of the new wake turbulence behind a single fractal tree (see section: Results (near-wake turbulence). The experiments of the full fractal canopy is scheduled and will be performed very soon. The results will be presented later.
Fractal Tree
The fractal tree model (shown in Figure 1) has five generations (N=5), with three branches at first generation and as scale-reduction factor 1/2 between adjacent generations. Its similarity fractal dimension is log3/log2=1.585. The first generation has 3 branches of diameter 28.8mm and the fifth generation (at the top) has 243 branches of diameter 1.8mm. Figure 2 shows typical cross-sections of five generations.
Figure 1. Fractal tree.
Figure 2. Typical cross-sections at five generations.
(Figures are cited from paper for Boundary-layer Meteorology, 2011)
Facilities
The experiments are carried out in the extension of the index-matched turbomachine facility in the Laboratory of Experimental Fluid Dynamics. The facility allows optical index-matching using NaI solution where unobstructed flow measurements for complex flow fields can be performed.
Figure 1. shows the set-up for the near wake measurement for a single fractal tree.
Figure 1. Set-up for new-wake measurement for a single tree.
(Figures are cited from paper for Boundary-layer Meteorology, 2011)
Experimental Setup (near-wake turbulence)
The set-up of the near-wake turbulence measurements behind a fractal tree is shown in Figure 1. The PIV measurements are conducted at 14 different x-y planes, parallel to the channel bottom. The CCD size of the camera is 4864*3248 pixel. The vector resolution is about 0.64mm with with 32*32 interrogation window and 50% overlap. The typical vector map is shown in Figure 2.
Figure 1. The set-up of the near-wake measurements.
Figure 2. Sample of Instantaneous velocity field.
(Figures are cited from paper for Boundary-layer Meteorology, 2011)
Results (near-wake turbulence)
The detailed flow fields are described in paper published in Boundary-Layer Meteorology (see section: Publications). Figure 1 shows the mean velocity profile (contour) behind the tree. Geometric features of the tree shape can be easily observed. We also described the evolutions of the mean velocity, Reynolds stresses, dispersive fluxes as a function of downstream location and height.
Interestingly, there is a clear linear relation between spanwise Reynolds shear stress and mean velocity gradient at every downstream location and elevations. The measured eddy viscosity and the Prandtl mixing length decreases as height increases (Figure 2).
To include the multiscale information, we propose two mixing length models based on the notion of superposition of scales. On is the spectral approach where the scales are estimated from radial spectra of the tree cross-section. Another model is derived analytically by using fractal tools.
The agreement between the measured and modeled mixing length indicates that the multiscale and clustering properties should be considered to estimate the mixing length when modeling canopies with multiscale objects.
More results are presented in the paper.
Figure 1. Mean streamwise velocity contour. (a) 3D. (b) 2D contour.
Figure 2. Measured eddy viscosity (a) and mixing length (b).
(Figures are cited from paper for Boundary-layer Meteorology, 2011)
Publications
Graham, J., Bai, K., Meneveau, C., & Katz, J. (2011). LES modeling and experimental measurement of boundary layer flow over multi-scale, fractal canopies. Direct and Large-Eddy Simulation VIII (pp. 233-238). Springer, Dordrecht.
Bai, K., Meneveau, C., & Katz, J. (2012). Near-wake turbulent flow structure and mixing length downstream of a fractal tree. Boundary-layer meteorology, 143(2), 285-308.