Statistics of Absolute and Relative Dispersion in the Atmospheric Convective Boundary Layer: A Large-Eddy Simulation Study

Abstract

The influence of the different scales of turbulent motion on plume dispersion in the atmospheric convective boundary layer (CBL) is studied by means of a large-eddy simulation (LES). In particular, the large-scale (meandering) and small-scale (relative diffusion) contributions are separated by analyzing dispersion in two reference systems: the absolute (fixed) coordinate system and the coordinate system relative to the plume's instantaneous center of mass. In the relative coordinate system, the (vertically) inhomogeneous meandering motion is removed, and only the small-scale, homogeneous turbulent motion contributes to the dispersion process.First, mean plume position, dispersion parameters (variance), and skewness of the plume position are discussed. The analysis of the third-order moments shows how the structure and the symmetry of scalar distribution are affected with respect to the turbulent characteristics of the CBL (inhomogeneity of the large-scale vertical motion) and the presence of the boundary conditions (surface and top of the CBL). In fact, the reflection of the plume by the CBL boundaries generates the presence of nonlinear crosscorrelation terms in the balance equation for the third-order moments of the plume position. As a result, the third-order moment of the absolute position is not balanced by the sum of the third-order moments of the meandering and relative plume position.Second, mean concentration and concentration fluctuations are calculated and discussed in both coordinate systems. The intensity of relative concentration fluctuation i cr , which quantifies the internal (in plume) mixing, is explicitly calculated. Based on these results, a parameterization for the probability distribution function (PDF) of the relative concentration is proposed, showing very good agreement with the LES results. Finally, the validity of Gifford's formula, which relates the absolute concentration's high-order moments to the relative concentration and the PDF of the plume centerline, is studied. It is found that due to the presence of the CBL boundaries, Gifford's formula is not able to reproduce correctly the value of the absolute mean concentration near the ground. This result is analyzed by showing that, when the plume is reflected by the CBL boundaries, the instantaneous relative plume width zЈ 2 r (t) departs from its mean value 2 r . By introducing the skewness of the relative plume position into a parameterization for the relative mean concentration, the results for the calculated mean concentration are improved.

Turbulent dispersion in cloud-topped boundary layers

“…This well mixed situation is characterized by three conditions: the mean plume height is approximately half the boundary layer height z≈0.5z i , secondly the vertical dispersion coefficient approaches the limit σ z /z i =1/ √ 12≈0.3 and finally the skewness of the plume should approach zero: S z ≈0. The results are in satisfactory agreement with other numerical studies by Nieuwstadt (1992) and Dosio and Vilà-Guerau de Arellano (2006), who in turn validated their results with experimental data from e.g. Willis and Deardorff (1978) and Briggs (1993).…”

Can statistics of turbulent tracer dispersion be inferred from camera observations of SO<sub>2</sub> in the ultraviolet?

“…For projected LES simulations and the simulated images, the vertical (in the images) plume centerline position, meandering, absolute and relative dispersions, and the skewness were calculated (see e.g. Dosio and de Arellano, 2006). Each pixel in the camera images and each projection from the LES simulations describe the integrated column amount (ρ L ) of the trace gas along the line of sight (dL):…”

“…Following Dosio and de Arellano (2006) we define the fluctuations of the absolute, relative and centerline positions:…”

Modeling the impact of sub-grid scale emission variability on upper-air concentration

“…The model has evolved over the years and has been successfully used to study many different processes in the ABL, from cloud dynamics (e.g., Cuijpers and Duynkerke, 1993;Siebesma and Cuijpers, 1995;Siebesma and Holtslag, 1996;van Zanten et al, 1999;Siebesma et al, 2003;Neggers et al, 2003), chemical reaction and radioactive decay in atmospheric turbulent environments (e.g., Meeder and Nieuwstadt, 2000;Vinuesa and Vilà-Guerau de Arellano, 2003;Jonker et al, 2004;Vinuesa and Vilà-Guerau de Arellano, 2005;Vinuesa and Galmarini, 2007), the influence of clouds on atmospheric chemistry (e.g., Vilà-Guerau de Arellano and Cuijpers, 2000;Jonker et al, 2004;Vilà-Guerau de Arellano et al, 2005), plume dispersion (e.g. Nieuwstadt, 1992a,b;Meeder and Nieuwstadt, 2000;Dosio et al, 2003;Vilà-Guerau de Arellano et al, 2004;Dosio et al, 2005;Dosio and Vilà-Guerau de Arellano, 2006), stable BL (e.g., Galmarini et al, 1998;Beare et al, 2006). For a detailed description of the model we refer the reader the above mentioned references.…”