On the Importance of Spatial Information in Modeling Scalar Dispersion in Canopy Flows

Lagrangian stochastic models are widely used for the estimation of scalar concentration in turbulent flows. These models were shown also to give good results for canopy flows, such as crop fields, forests and urban areas, in spite of their high inhomogeneity and anisotropy. However, these models are usually based on partial information about the flow. Velocity measurements are limited in most cases to the time statistics of turbulence at one location at a time. Using such data requires some assumptions when modeling scalar dispersion in canopy environments; for example, isotropy of the dissipation flux and the application of the Taylor's frozen turbulence hypothesis, which is not valid for canopy flows. Our study is unique since the flow field is based on detailed measurements above and within a canopy model. The canopy model is made of randomly distributed thin microscope slides, in an open channel, using a particle image velocimetry (PIV) system, and therefore serves as an excellent starting point for modeling particle transport. The advantage is that a velocity map, which contains thousands of velocity vectors, can be obtained at each instantaneous measurement. Repeating the measurement at many cross-sections along the channel width results in a complete description of the averaged flow. The PIV instantaneous velocity maps provide both single-point and two-point statistics in a high spatial resolution, which give reliable estimation for the time and length scales of turbulence and the dissipation rate. A Lagrangian stochastic model of scalar dispersion, based on the solution of the general form of the Langevin equation, is applied using the PIV flow statistics, which takes into account the anisotropic nature of the canopy flow. Using this model allows examining several assumptions of stochastic modeling in canopy flows, as well as the importance of the detailed spatial information about the flow. The model results show that while the value of the stochastic term of the Langevin equation can be obtained from the vertical flow components alone, and while both one-point and two-point correlations generate similar predictions, accurate modeling needs a flow representation that is based on a complete volume averaging. It will be demonstrated that one single profile, positioned arbitrarily, is likely to generate incorrect results.