Analytical offline approach for concentration fluctuations and higher order concentration moments

Concentration Fluctuations and Odor Dispersion in Lagrangian Models

“…However, the first two moments fully define a gamma distribution function, which describe the distribution of instantenous concentrations for a wide scale of ranges [62,63]. This agrees with observed scaling relations between the first two moments and higher moments [19]. Marro et al (2018) [64] took advantage of these results and proposed a so-called VPΓ model, which utilizes the VPA model for the calculation of the two first moments and estimates the third and fourth moment using the gamma function hypothesis.…”

“…Many Lagrangian models have been developed for the second-and higher-order moments of the concentration pdf over the last 10 years. Thomson (1990) [7] and Borgas and Sawford (1994) [8] proposed the two-particle model, Pope (1985) and Cassiani et al (2005Cassiani et al ( , 2007, Leuzzi et al (2012) [8][9][10][11][12] the pdf method, while the fluctuating plume model was suggested by Yee et al (1994), Yee and Wilson (2000), Luhar et al (2000), Franzese (2003), Mortarini et al (2009), Ferrero et al (2013), Bisignano et al (2014), Marro et al(2015) [13][14][15][16][17][18][19][20]. Manor (2014) [21] used a Lagrangian particle model to simulate the concentration variance dispersion and Ferrero et al (2017) [22] suggested a formulation for the variance dissipation time scale to be used in the same model.…”

Atmospheric Pollutant Dispersion over Complex Terrain: Challenges and Needs for Improving Air Quality Measurements and Modeling

“…In particular, when the ratio of the chemical reaction rate to the turbulent mixing rate, the Damköhler number, is small and the equilibrium is almost instantaneously reached, chemistry is not affected by the turbulent dispersion, but when the Damköhler number is ∼1 or larger, the segregation of the reactants may be important [231]. In this case, concentration fluctuations are needed and Lagrangian models able to predict concentration moments of orders higher than the first (see, for instance, [228,[232][233][234][235][236][237]) can be successfully used. On the other hand, Eulerian models provide only mean concentrations and cannot take into account this effect.…”

“…Many models have been developed for the second and higher order moments of the concentration PDF over the last ten years. Thomson [256] and Borgas and Sawford [257] proposed the two-particle model, Pope [258] and Cassiani et al [259] proposed the PDF method, while the fluctuating plume model was suggested by Ferrero et al [230], Luhar et al [232], Franzese [233], Mortarini et al [234], Bisignano et al [235], Yee et al [260], and Yee and Wilson [261]. While the two-particle model can be applied only in homogenous and isotropic conditions, the fluctuating plume model is able to take into account the flow inhomogeneity and, as a consequence, is suitable for applications in complex terrain.…”

A 3D Lagrangian stochastic particle model for the concentration variance dispersion

“…The further extension to Lagrangian meandering plume model is due to Luhar et al (2000) and Franzese (2003). Mortarini et al (2009) extended the approach suggested by Franzese (2003) by applying the fluctuating plume model to the turbulent flow generated in a simulated canopy, while Cassiani and Giostra (2002) proposed a similar model that was based on a linear compression of the mean concentration PDF, which enables rapid evaluation of higher-order concentration moments (Bisignano et al 2014). Recent development can be found in Marro et al (2015Marro et al ( , 2018.…”