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 usually investigated by using two different approaches: in the Eulerian framework, statistical properties are calculated in a fixed reference frame, whereas in the Lagrangian framework statistical properties are calculated in a reference frame moving with the flow. Lagrangian framework is the most natural approach in theoretical studies of turbulent dispersion, whereas the Eulerian approach is most commonly used in field experiments.

In this study the relationship between Lagrangian properties (autocorrelation functions) and dispersion characteristics (particles' displacement) is studied trough Taylor's diffusion relationship. By using of Large-Eddy Simulation (LES) the dispersion process in the non-isotropic atmospheric Convective Boundary Layer (CBL) is analyzed. Lagrangian statistics are derived by tracking the trajectories of numerous particles released at different heights in the turbulent flow. Spectra analysis is conducted in both the Eulerian and Lagrangian frameworks, autocorrelations are calculated and the integral length and time scales derived.

Results show that for the horizontal motion, Taylor's relationship is satisfied. The vertical motion, however, is influenced by the non-homogeneity of the flow and limited by the ground and the inversion of the CBL. As a result, the Lagrangian autocorrelation does not follow an exponential function and its integral becomes zero at large times. If distinction is made between free and bounded motion, a better agreement between Taylor's relationship and the particles' vertical displacement is found. Relationship between Eulerian and Lagrangian frameworks are analyzed by calculating the ratio ß between Lagrangian and Eulerian timescales. Results show that the integral time scales are mainly constant with height for z/zi<0.7. In the upper layer of the CBL, the presence of the inversion transforms vertical motion into horizontal. As a result, the horizontal time scale increases with height, whereas the vertical one is reduced. Current parameterizations for the ratio between Eulerian and Lagrangian time scale have been tested against the LES results showing satisfactorily agreement at heights z/zi <0.7.