Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence
The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity difference Δur is derived through a stat...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Engineering |
| Online Access: | http://dx.doi.org/10.1155/2013/653027 |
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| author | Nicola de Divitiis |
| author_facet | Nicola de Divitiis |
| author_sort | Nicola de Divitiis |
| collection | DOAJ |
| description | The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity difference Δur is derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics of Δur and adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade. |
| format | Article |
| id | doaj-art-abf1a870a2924c6bb39bef073d3fd6f8 |
| institution | Kabale University |
| issn | 2314-4904 2314-4912 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Engineering |
| spelling | doaj-art-abf1a870a2924c6bb39bef073d3fd6f82025-02-03T07:24:28ZengWileyJournal of Engineering2314-49042314-49122013-01-01201310.1155/2013/653027653027Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic TurbulenceNicola de Divitiis0Dipartimento di Ingegneria Meccanica e Aerospaziale, “La Sapienza” University, Via Eudossiana 18, 00184 Rome, ItalyThe purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity difference Δur is derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics of Δur and adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.http://dx.doi.org/10.1155/2013/653027 |
| spellingShingle | Nicola de Divitiis Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence Journal of Engineering |
| title | Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence |
| title_full | Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence |
| title_fullStr | Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence |
| title_full_unstemmed | Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence |
| title_short | Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence |
| title_sort | refinement of a previous hypothesis of the lyapunov analysis of isotropic turbulence |
| url | http://dx.doi.org/10.1155/2013/653027 |
| work_keys_str_mv | AT nicoladedivitiis refinementofaprevioushypothesisofthelyapunovanalysisofisotropicturbulence |