Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part III: Stochastic Modelling

Abstract

We analyze the reliability of the Lagrangian stochastic micromixing method in predicting higher-order statistics of the passive scalar concentration induced by an elevated source (of varying diameter) placed in a turbulent boundary layer. To that purpose we analyze two different modelling approaches by testing their results against the wind-tunnel measurements discussed in Part I (Nironi et al., Boundary-Layer Meteorology, 2015, Vol.156, 415-446). The first is a probability density function (PDF) micromixing model that simulates the effects of the molecular diffusivity on the concentration fluctuations by taking into account the background particles. The second is a new model, named VPΓ , conceived in order to minimize the computational costs. This is based on the volumetric particle approach providing estimates of the first two concentration moments with no need for the simulation of the background particles. In this second approach, higher-order moments are computed based on the estimates of these two moments and under the assumption that the concentration PDF is a Gamma distribution. The comparisons concern the spatial distribution of the first four moments of the concentration and the evolution of the PDF along the plume centreline. The novelty of this work is twofold: i) we perform a systematic comparison of the results of micro-mixing Lagrangian models against experiments providing profiles of the first four moments of the concentration within an inhomogeneous and anisotropic turbulent flow, and ii) we show the reliability of the VPΓ model as an operational tool for the prediction of the PDF of the concentration.

Solution for the statistical moments of scalar turbulence

“…σ ur is the root-mean square of the fluctuations of relative velocity, i.e., the difference between the turbulent velocity and the instantaneous velocity of the plume centroid. This latter quantity is usually modeled as [23,45]…”

“…is the inertial formulation for a dispersion from a finite source size [8], t f = x/U is the flight time, and T L = 2σ 2 u /C 0 ε is the Lagrangian timescale. The Richardson and Kolmogorov constants read C r = 0.3 and C 0 = 4.5, respectively [23], while the constant α = 0.65 for Eq. (11) is obtained from a best fit with experiments.…”

“…The computation of C and σ 2 can be performed by means of a variety of numerical approaches (e.g., Refs. [20][21][22][23]). However, for operational purposes, it is worth disposing of analytical solutions for reference configurations, such as that of a localized release within the atmospheric boundary layer (see Fig.…”

Characterising vertical turbulent dispersion by observing artificially released SO<sub>2</sub> puffs with UV cameras

“…Therefore parametrized expressions of relative dispersion are used in defining simplified models of concentration fluctuations (e.g. Luhar et al, 2000;Yee and Wilson, 2000;Cassiani and Giostra, 2002;Sawford, 2004;Cassiani et al, 2005;Marro et al, 2015Marro et al, , 2018.…”

“…However, C r and the directly related relative dispersion 20 are important for models as the relative dispersion defines the effective rate of mixing of a puff and therefore the decay rate of concentration fluctuations (e.g. Sawford, 2004;Cassiani et al, 2005;Pinsky et al, 2016;Marro et al, 2018).…”