Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion
An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. The solution approach is to identify a representation of the Dirac delta function for large times...
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| Language: | English |
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Academia.edu Journals
2024-05-01
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| Series: | Academia Environmental Sciences and Sustainability |
| Online Access: | https://www.academia.edu/118648389/Asymptotic_solution_for_turbulent_variances_application_to_convergence_of_averages_and_particle_dispersion |
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| author | Gervásio Annes Degrazia Michel Stefanello Felipe Denardin Costa Luís Gustavo Nogueira Martins Otávio Costa Acevedo |
| author_facet | Gervásio Annes Degrazia Michel Stefanello Felipe Denardin Costa Luís Gustavo Nogueira Martins Otávio Costa Acevedo |
| author_sort | Gervásio Annes Degrazia |
| collection | DOAJ |
| description |
An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. The solution approach is to identify a representation of the Dirac delta function for large times in the same integral occurring in both variances. This particular function acts as an effective filter and provides a way to obtain an analytical solution. Considering these asymptotic dispersion parameters in a Gaussian diffusion model, analysis of the simulated concentration results shows that the model reproduces well the experimental ground-level concentration data. The variance between the temporal and ensemble averages is evaluated using turbulent observational data collected in a convective boundary layer. The results show that the difference between the temporal and ensemble means is of the order of 5% for an average time window of 1800 s. The present development can be used in a variety of situations involving different types of turbulence. |
| format | Article |
| id | doaj-art-ba70457dd37d4854bd651171ca58f87e |
| institution | Kabale University |
| issn | 2997-6006 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Academia.edu Journals |
| record_format | Article |
| series | Academia Environmental Sciences and Sustainability |
| spelling | doaj-art-ba70457dd37d4854bd651171ca58f87e2025-02-10T23:01:59ZengAcademia.edu JournalsAcademia Environmental Sciences and Sustainability2997-60062024-05-011110.20935/AcadEnvSci6217Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersionGervásio Annes Degrazia0Michel Stefanello1Felipe Denardin Costa2Luís Gustavo Nogueira Martins3Otávio Costa Acevedo4Department of Physics, Federal University of Santa Maria, Santa Maria, 97105-900, Brazil.Department of Physics, Federal University of Santa Maria, Santa Maria, 97105-900, Brazil.Department of Physics, Federal University of Santa Maria, Santa Maria, 97105-900, Brazil.Department of Physics, Federal University of Santa Maria, Santa Maria, 97105-900, Brazil.Department of Physics, Federal University of Santa Maria, Santa Maria, 97105-900, Brazil. An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. The solution approach is to identify a representation of the Dirac delta function for large times in the same integral occurring in both variances. This particular function acts as an effective filter and provides a way to obtain an analytical solution. Considering these asymptotic dispersion parameters in a Gaussian diffusion model, analysis of the simulated concentration results shows that the model reproduces well the experimental ground-level concentration data. The variance between the temporal and ensemble averages is evaluated using turbulent observational data collected in a convective boundary layer. The results show that the difference between the temporal and ensemble means is of the order of 5% for an average time window of 1800 s. The present development can be used in a variety of situations involving different types of turbulence.https://www.academia.edu/118648389/Asymptotic_solution_for_turbulent_variances_application_to_convergence_of_averages_and_particle_dispersion |
| spellingShingle | Gervásio Annes Degrazia Michel Stefanello Felipe Denardin Costa Luís Gustavo Nogueira Martins Otávio Costa Acevedo Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion Academia Environmental Sciences and Sustainability |
| title | Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion |
| title_full | Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion |
| title_fullStr | Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion |
| title_full_unstemmed | Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion |
| title_short | Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion |
| title_sort | asymptotic solution for turbulent variances application to convergence of averages and particle dispersion |
| url | https://www.academia.edu/118648389/Asymptotic_solution_for_turbulent_variances_application_to_convergence_of_averages_and_particle_dispersion |
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