Relating Eulerian and Lagrangian Statistics for the Turbulent Dispersion in the Atmospheric Convective Boundary Layer

Eulerian and Lagrangian statistics in the atmospheric convective boundary layer (CBL) are studied by means of large eddy simulation (LES). Spectra analysis is performed in both the Eulerian and Lagrangian frameworks, autocorrelations are calculated, and the integral length and time scales are derived. Eulerian statistics are calculated by means of spatial and temporal analysis in order to derive characteristic length and time scales. Taylor’s hypothesis of frozen turbulence is investigated, and it is found to be satisfied in the simulated flow. Lagrangian statistics are derived by tracking the trajectories of numerous particles released at different heights in the turbulent flow. The relationship between Lagrangian properties (autocorrelation functions) and dispersion characteristics (particles’ displacement) is studied through Taylor’s diffusion relationship, with special emphasis on the difference between horizontal and vertical motion. Results show that for the horizontal motion, Taylor’s relationship is satisfied. The vertical motion, however, is influenced by the inhomogeneity of the flow and limited by the ground and the capping inversion at the top of the CBL. The Lagrangian autocorrelation function, therefore, does not have an exponential shape, and consequently, the integral time scale is zero. If distinction is made between free and bounded motion, a better agreement between Taylor’s relationship and the particles’ vertical displacement is found. Relationships between Eulerian and Lagrangian frameworks are analyzed by calculating the ratio β between Lagrangian and Eulerian time scales. Results show that the integral time scales are mainly constant with height for z/zi < 0.7. In the upper part of the CBL, the capping inversion transforms vertical motion into horizontal motion. As a result, the horizontal time scale increases with height, whereas the vertical one is reduced. Current parameterizations for the ratio between the Eulerian and Lagrangian time scales have been tested against the LES results showing satisfactory agreement at heights z/zi < 0.7.