Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces
Turbulent systems represent a complex and ubiquitous phenomenon in various natural and engineered environments. This study investigates the dynamics of turbulent systems through the lens of four fundamental theorems. The first theorem establishes a spectral decomposition of the velocity correlation...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Viçosa (UFV)
2024-05-01
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| Series: | The Journal of Engineering and Exact Sciences |
| Subjects: | |
| Online Access: | https://periodicos.ufv.br/jcec/article/view/18659 |
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| _version_ | 1832569800250884096 |
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| author | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales |
| author_facet | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales |
| author_sort | Rômulo Damasclin Chaves dos Santos |
| collection | DOAJ |
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Turbulent systems represent a complex and ubiquitous phenomenon in various natural and engineered environments. This study investigates the dynamics of turbulent systems through the lens of four fundamental theorems. The first theorem establishes a spectral decomposition of the velocity correlation function, shedding light on the coherent and incoherent structures within turbulent flows. The second theorem delves into the energy distribution in Sobolev spaces, providing insights into the regularity and properties of turbulent solutions. Expanding on these findings, the third theorem explores the influence of external forcing on energy distribution, elucidating how external factors shape turbulent behavior. Building upon these insights, the fourth theorem integrates the concepts from the previous theorems, describing the interplay between spectral decomposition, energy distribution, and external forcing effects in turbulent systems. This comprehensive analysis offers a deeper understanding of turbulent dynamics, with implications for fields such as fluid mechanics, atmospheric science, and engineering. By elucidating the underlying mechanisms governing turbulent behavior, this study paves the way for improved modeling, prediction, and control of turbulent systems in various practical applications.
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| format | Article |
| id | doaj-art-65a0a893e3c6468c9d4318601c8e6bb5 |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-65a0a893e3c6468c9d4318601c8e6bb52025-02-02T19:53:42ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752024-05-0110610.18540/jcecvl10iss6pp18659Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev SpacesRômulo Damasclin Chaves dos SantosJorge Henrique de Oliveira Sales0State University of Santa Cruz - DCEX Turbulent systems represent a complex and ubiquitous phenomenon in various natural and engineered environments. This study investigates the dynamics of turbulent systems through the lens of four fundamental theorems. The first theorem establishes a spectral decomposition of the velocity correlation function, shedding light on the coherent and incoherent structures within turbulent flows. The second theorem delves into the energy distribution in Sobolev spaces, providing insights into the regularity and properties of turbulent solutions. Expanding on these findings, the third theorem explores the influence of external forcing on energy distribution, elucidating how external factors shape turbulent behavior. Building upon these insights, the fourth theorem integrates the concepts from the previous theorems, describing the interplay between spectral decomposition, energy distribution, and external forcing effects in turbulent systems. This comprehensive analysis offers a deeper understanding of turbulent dynamics, with implications for fields such as fluid mechanics, atmospheric science, and engineering. By elucidating the underlying mechanisms governing turbulent behavior, this study paves the way for improved modeling, prediction, and control of turbulent systems in various practical applications. https://periodicos.ufv.br/jcec/article/view/18659Turbulent systemsMixed convectionSpectral decompositionSobolev spaces |
| spellingShingle | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces The Journal of Engineering and Exact Sciences Turbulent systems Mixed convection Spectral decomposition Sobolev spaces |
| title | Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces |
| title_full | Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces |
| title_fullStr | Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces |
| title_full_unstemmed | Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces |
| title_short | Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces |
| title_sort | turbulent system dynamics an introduction to spectral decomposition and external forcing in sobolev spaces |
| topic | Turbulent systems Mixed convection Spectral decomposition Sobolev spaces |
| url | https://periodicos.ufv.br/jcec/article/view/18659 |
| work_keys_str_mv | AT romulodamasclinchavesdossantos turbulentsystemdynamicsanintroductiontospectraldecompositionandexternalforcinginsobolevspaces AT jorgehenriquedeoliveirasales turbulentsystemdynamicsanintroductiontospectraldecompositionandexternalforcinginsobolevspaces |