Turbulence-obstacle interactions in the Lagrangian framework: Applications for stochastic modeling in canopy flows

Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood how particular features of highly inhomogeneous canopy flows affect the Lagrangian statistics. In this work, we study Lagrangian short-time statistics by analyzing empirical Lagrangian trajectories in subvolumes of space that are small in comparison with the canopy height. For the analysis we used 3D Lagrangian trajectories measured in a dense canopy flow model in a wind-tunnel, using an extended version of real-time 3D particle tracking velocimetry. One of our key results is that the random turbulent fluctuations due to the intense dissipation were more dominant than the flow's inhomogeneity in affecting the short-time Lagrangian statistics. This amounts to a so-called quasihomogeneous regime of Lagrangian statistics at small scales. Using the Lagrangian dataset, we calculate the Lagrangian autocorrelation function and the second-order Lagrangian structure-function and extract associated parameters, namely, a Lagrangian velocity decorrelation timescale, Ti, and the Kolmogorov constant, C0. We demonstrate that in the quasihomogeneous regime, both these functions are well represented using a second-order Lagrangian stochastic model that was designed for homogeneous flows. Furthermore, we show that the spatial variations of the Lagrangian separation of scales, Ti/τη, and the Kolmogorov constant, C0, cannot be explained by the variation of the Reynolds number, Reλ, in space, and that Ti/τη was small as compared with homogeneous turbulence predictions at similar Reλ. We thus hypothesize that these characteristics occurred due to the injection of kinetic energy at small scales due to the so-called "wake-production"process, and we show empirical results supporting our hypothesis. These findings shed light on key features of Lagrangian statistics in flows with intense dissipation, and have direct implications for modeling short term dispersion in such complex environments.