# DEVELOPMENT OF A MATHEMATICAL MODEL TO DESCRIBE THE CONTAMINANT DISPERSION IN MEANDERING CONDITIONS

## Authors

• Michel Baptistella Stefanello Aluno do PPGFis, Universidade Federal de Santa Maria, Santa Maria, Brasil
• Gervásio Annes Degrazia Professor do Departamento de Física, Universidade Federal de Santa Maria, Santa Maria, Brasil
• Celene Buriol Professora do Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria, Brasil
• Lilian Moor Aluna do PPGFis, Universidade Federal de Santa Maria, Santa Maria, Brasil
• Jonas Carvalho Professor da Faculdade de Meteorologia, Universidade Federal de Pelotas, Pelotas, Brasil
• Luca Mortarini Pesquisador do Istituto di Scienzedell’Atmosfera e del Clima (CNR), Torino, Italy
• Umberto Rizza Pesquisador do Istituto di Scienzedell’Atmosfera e del Clima, (CNR), Lecce, Italy

## Keywords:

Meandering. Autocorrelation function. Langevin equation.

## Abstract

In this work it’s derived a mathematical model to describe the meandering contaminants dispersion in the planetary boundary layer.  The model employs a heuristic functional form for the velocity autocorrelation function which describes the negatives lobes observed in meandering data. Furthermore, the model is derived from the linearization of the Langevin equation. The mathematical equations, that represent the longitudinal and lateral wind components describe the bi-dimensional pattern of the meandering flow and can be utilized to calculate the contaminant concentrations occurring in situations in which the meandering phenomenon plays a decisive role.

## References

Carvalho, J. C. ; Vilhena, M. T. ; Degrazia, G. A. ; Sallet, M. A General Lagrangian Approach to Simulate Pollutant Dispersion in Atmosphere for Low-wind Condition. American Journal of Environmental Engineering, v. 3, p. 8-12, 2013.

Carvalho, J.C. and Vilhena, M. T. M. B. Pollutant dispersion simulation for low wind speed condition by the ILS method", Atmospheric Environment, vol.39, pp.6282-6288, 2005.

Frenkiel, F. N. Turbulent diffusion: mean concentration distribution in a flow field of homogeneous turbulence. Advances in Applied Mechanics, 3, 1953. 61–107.

Moor, L., Degrazia, G., Stefanello, M., Mortarini, L., Acevedo, O., Maldaner, S., Szinvelski, C., Roberti, D., Buligon, L., Anfossi, D. (2015). Proposal of a new autocorrelation function in low wind speed conditions. Physica A: Statistical Mechanics and its Applications, 438, 286–292.

Mortarini, L., Anfossi, D. (2015). Proposal of an empirical velocity spectrum formula in low-wind speed conditions. Quarterly Journal of the Royal Meteorological Society, 141(686), 85–97.

Mortarini, L., Ferrero, E., Falabino, S., Trini Castelli, S., Richiardone, R., Anfossi, D. (2013). Low-frequency processes and turbulence structure in a perturbed boundary layer. Quarterly Journal of the Royal Meteorological Society, 139(673), 1059–1072

2016-07-20

## How to Cite

Stefanello, M. B., Degrazia, G. A., Maldaner, S., Buriol, C., Moor, L., Carvalho, J., Mortarini, L., & Rizza, U. (2016). DEVELOPMENT OF A MATHEMATICAL MODEL TO DESCRIBE THE CONTAMINANT DISPERSION IN MEANDERING CONDITIONS. Ciência E Natura, 38, 326–329. https://doi.org/10.5902/2179460X20248

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