On local isotropy and scale dependence of pair dispersion in turbulent canopy flows

Abstract: Canopy flows in the atmospheric surface layer play important economic and ecological roles, governing the dispersion of passive scalars in the environment. The interaction of high-velocity fluid and large-scale surface-mounted obstacles in canopy flows produces drag and causes intense, inhomogeneous, and anisotropic turbulence. In this work, we focus on the turbulent dispersion of passive scalars by studying the ``pair dispersion'' - a statistical measure of relative motion between particles. We analyze the results of a 3D-PTV experiment in a wind tunnel canopy flow, focusing on small scales. We confirm the existence of local isotropy of pair dispersion at scales smaller than a characteristic shear length scale $L_\Gamma=(\epsilon/\Gamma^3)^{1/2}$, where $\epsilon$ and $\Gamma$ are the mean dissipation rate and shear rate, respectively. Furthermore, we show that pair dispersion in this locally isotropic regime is a scale-dependent super-diffusive process, similar to what occurs in homogeneous isotropic turbulent flows. In addition, we measure the pair relative velocity correlation function, showing that its de-correlation occurs in the locally isotropic regime, and discuss the implications of this observation for modeling pair dispersion. Thus, our study extends the fundamental understanding of turbulent pair dispersion to the anisotropic, inhomogeneous, turbulent canopy flow, bringing valuable information for modeling scalar dispersion in the atmospheric surface layer.