Turbulence -- Obstacle Interactions in the Lagrangian Framework: Applications for Stochastic Modeling in Canopy Flows

Abstract

Lagrangian stochastic models are widely used for making predictions and in the analysis of turbulent dispersion in complex environments, such as the terrestrial canopy flows. However, due to a lack of empirical data, how particular features of canopy phenomena affect the parameterizations of Lagrangian statistics is still not known. In the following work, we consider the impact of obstacle wakes on Lagrangian statistics. Our analysis is based on 3D trajectories measured in a wind-tunnel canopy flow model, where we estimated Lagrangian statistics directly. In particular, we found that both the Lagrangian autocorrelation and the second order structure functions could be well represented using a second-order Lagrangian stochastic model. Furthermore, a comparison of our empirically estimated statistics with predictions for the case of homogeneous flow shows that decorrelation times of Lagrangian velocity were very short and that the Kolmogorov constant, \(C_0\), was not a function of \(Re_\lambda\) alone in our canopy flow. Our subsequent analysis indicated that this was not a result of flow inhomogeneity, but instead a result of the wake production. Thus, our empirical study suggests that the wake-production can lead to a so-called `rapid decorrelation' in which both \(C_0\) and the separation of scales \(T/\tau_\eta\) (\(T\) being a Lagrangian velocity decorrelation timescale) are not determined by \(Re_\lambda\) alone, and may cause finite Reynolds number effects to occur even at high Reynolds number canopy flows.