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

TL;DR

This study investigates how turbulence interacts with obstacles in canopy flows using Lagrangian trajectories, revealing that small-scale turbulence dominates short-term statistics and that existing models for homogeneous flows can be applied in certain regimes.

Contribution

It provides empirical evidence that small-scale turbulence governs Lagrangian statistics in canopy flows and extends the applicability of homogeneous flow models to inhomogeneous canopy turbulence.

Findings

Turbulent fluctuations due to dissipation dominate over flow inhomogeneity.

Lagrangian stochastic models for homogeneous flows fit data in the quasi-homogeneous regime.

Spatial variations in scale separation and Kolmogorov constant are not explained by Reynolds number variations.

Abstract

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 sub-volumes 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 (3D-PTV). 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 quasi-homogeneous 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, $T_i$, and the Kolmogorov constant, $C_0$. We demonstrate that in the quasi-homogeneous 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, $T_i/\tau_\eta$, and the Kolmogorov constant, $C_0$, cannot be explained by the variation of the Reynolds number, $Re_\lambda$, in space, and that $T_i/\tau_\eta$ was small as compared with homogeneous turbulence predictions at similar $Re_\lambda$. We thus hypothesize that this occurred due to the so-called "wake production", and show empirical results supporting our hypothesis.