Turbulent Flow Structure Inside a Canopy with Complex Multi-Scale Elements

Abstract

Particle image velocimetry laboratory measurements are carried out to study mean flow distributions and turbulent statistics inside a canopy with complex geometry and multiple scales consisting of fractal, tree-like objects. Matching the optical refractive indices of the tree elements with those of the working fluid provides unobstructed optical paths for both illuminations and image acquisition. As a result, the flow fields between tree branches can be resolved in great detail, without optical interference. Statistical distributions of mean velocity, turbulence stresses, and components of dispersive fluxes are documented and discussed. The results show that the trees leave their signatures in the flow by imprinting wake structures with shapes similar to the trees. The velocities in both wake and non-wake regions significantly deviate from the spatially-averaged values. These local deviations result in strong dispersive fluxes, which are important to account for in canopy-flow modelling. In fact, we find that the streamwise normal dispersive flux inside the canopy has a larger magnitude (by up to four times) than the corresponding Reynolds normal stress. Turbulent transport in horizontal planes is studied in the framework of the eddy viscosity model. Scatter plots comparing the Reynolds shear stress and mean velocity gradient are indicative of a linear trend, from which one can calculate the eddy viscosity and mixing length. Similar to earlier results from the wake of a single tree, here we find that inside the canopy the mean mixing length decreases with increasing elevation. This trend cannot be scaled based on a single length scale, but can be described well by a model, which considers the coexistence of multi-scale branches. This agreement indicates that the multi-scale information and the clustering properties of the fractal objects should be taken into consideration in flows inside multi-scale canopies.