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, C0, was not a function of Re λ 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 C0 and the separation of scales T /τη (T being a Lagrangian velocity decorrelation timescale) are not determined by Re λ alone, and may cause finite Reynolds number effects to occur even at high Reynolds number canopy flows.

On small-scale and large-scale intermittency of Lagrangian statistics in canopy flow

“…It shows four autocorrelation functions: three for the increments of each of the velocity components (, and ) and one for increments of the magnitude of the velocity vector, taking the time lag (the velocity difference can be used as a proxy for the acceleration because, as Voth, Satyanarayan & Bodenschatz (1998) and Shnapp et al. (2020) showed, at such small time-lags the acceleration is still correlated, so approximately ). While the three components’ velocity increments became decorrelated () at roughly , the velocity magnitude difference retained correlation with itself over the whole range of the measurement, with the minimum value of around .…”

“…Lagrangian trajectories in a canopy flow were analysed using the results of a wind tunnel, three-dimensional particle tracking velocimetry (3D-PTV) experiment. The full experimental details are given in Shnapp et al (2019), and Lagrangian statistics were analysed in Shnapp et al (2020). For brevity, only the information relevant to this work shall be repeated here.…”

“…This work presents an analysis of Lagrangian statistics in a canopy flow using empirical results from a recent wind tunnel experiment (Shnapp et al 2019). The existence of small-scale intermittency is demonstrated in § 3.1, and the results are compared with previous studies from homogeneous isotropic turbulence (HIT) flows.…”

“…Other than that, there is a lack of studies that focus on large-scale intermittency in the Lagrangian framework. In particular, there are no empirical investigations of intermittency in Lagrangian statistics in canopy flows despite its importance to Lagrangian stochastic models with applications for dispersion and mixing in the environment (Wilson & Sawford 1996;Reynolds 1998;Duman et al 2016;Keylock et al 2020;Shnapp et al 2020;Viggiano et al 2020).…”

The Micrometeorology of the Haifa Bay Area and Mount Carmel during the Summer

“…Such a model should account for scenarios that correspond to the specific atmospheric conditions of this area [7]. Such scenarios should be based on comprehensive information on the average wind field, the statistical parameters of the turbulence as well as the influence of the heterogeneous canopy on these variables [8,9].…”