Relationship between Eulerian and Lagrangian Statistics in the Study of Atmospheric Dispersion in the Convective Boundary Layer: a Large-eddy Simulation Study

Atmospheric dispersion is a topic of great importance especially in relation to pollutant transport. Two different approaches, known as the Eulerian and the Lagrangian frameworks, are used to describe this process. In the Eulerian framework, statistical properties are calculated in a fixed reference frame. This approach is most commonly used in field experiments as well as in laboratory experiments or Eulerian numerical models. In the Lagrangian framework the statistical properties are calculated in a reference frame which moves with the flow. This is the most natural approach for theoretical investigation of turbulent dispersion, as in the works by Taylor (1921) who established seminal theoretical relationships between dispersion parameters and turbulent characteristics. Experimental measures of Lagrangian statistics in the atmospheric Convective Boundary Layer (CBL) are very difficult to obtain, (Hanna, 1981), whereas experiment with grid-generated isotropic turbulence (e.g. Sato and Yamamoto, 1987) are only partially representative of the turbulent motion in the CBL. A suitable approach for studying Lagrangian statistics in the CBL is by Large Eddy Simulation (LES), i.e. trajectories of particles released in a numerically generated turbulent flow are tracked in space and time. In this study we used a LES to address three main research issues: First, the turbulent characteristics of the flow are studied in both Eulerian and Lagrangian frameworks by analyzing velocity autocorrelations and calculating integral scales. Second, the relationship between flow properties (autocorrelations) and dispersion characteristics (particles’ displacements) is discussed through Taylor’s analysis of turbulent dispersion (Taylor, 1921). The influence of the asymmetry of the CBL flow on dispersion is studied, with the focus being on the difference between horizontal and vertical motion. Finally, the relationship between Eulerian and Lagrangian frameworks is studied by calculating the ratio β between the Lagrangian and Eulerian time scales.