Physically Parameterized Fourth-Order Retention and Scaling Analysis in Bi-Flux Turbulent Dispersion for the Planetary Boundary Layer

Matheus Henrique S. Siqueira; Roseane A. S. Albani; Antônio J. Silva Neto; Davidson M. Moreira

doi:10.63595/vetor.v36i1.20896

Authors

Matheus Henrique S. Siqueira Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0000-0003-2178-9779
Roseane A. S. Albani Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0000-0002-2091-194X
Antônio J. Silva Neto Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0000-0002-9616-6093
Davidson M. Moreira SENAI CIMATEC, Salvador, Bahia, Brazil https://orcid.org/0000-0002-0902-5218

DOI:

https://doi.org/10.63595/vetor.v36i1.20896

Keywords:

Atmospheric Dispersion, Bi-Flux Model, Anomalous Diffusion

Abstract

Classical Fickian diffusion theory often fails to capture the complex structure of turbulent dispersion in the Planetary Boundary Layer (PBL), particularly regarding the description of memory effects and plume retention. This work investigates the Bi-flux dispersion theory, which extends the advection-diffusion equation by incorporating a fourth-order derivative term to model non-Fickian transport phenomena. Unlike previous analytical approaches limited to constant coefficients, this study develops a numerical model using a high-order implicit finite difference scheme that incorporates realistic height-dependent profiles for both wind speed and vertical eddy diffusivity. A novel physical parameterization is proposed for the fourth-order retention coefficient, defined as K_z2 ∝ u_*|L|³, linking the non-Fickian mechanism to the local atmospheric turbulence scales (friction velocity and Monin-Obukhov length). The model was validated against the Copenhagen Experiment dataset. A sensitivity analysis of the partition parameter β revealed an optimal performance at β=0.99. The results demonstrate that the physically parameterized Bi-flux model significantly outperforms the classical Fickian formulation (β=1.0), achieving a 24.1% reduction in the Normalized Mean Square Error (NMSE) and a 70.4% improvement in the Fractional Standard Deviation (FS). These findings confirm that the inclusion of an atmospheric-scaled fourth-order term effectively preserves the internal variance of the plume, offering a superior predictive capability for pollutant dispersion in unstable boundary layers.

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