Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence
The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed chaos, this statistics is here analyzed assuming that the entr...
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/2365602 |
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| author | Nicola de Divitiis |
| author_facet | Nicola de Divitiis |
| author_sort | Nicola de Divitiis |
| collection | DOAJ |
| description | The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed chaos, this statistics is here analyzed assuming that the entropy associated with the fluid kinematic state is maximum. The distribution of the local Lyapunov exponents results in an unsymmetrical uniform function in a proper interval of variation. From this PDF, we determine the relationship between average and maximum Lyapunov exponents and the longitudinal velocity correlation function. This link, which in turn leads to the closure of von Kármán–Howarth and Corrsin equations, agrees with results of previous works, supporting the proposed PDF calculation, at least for the purposes of the energy cascade main effect estimation. Furthermore, through the property that the Lyapunov vectors tend to align the direction of the maximum growth rate of trajectories distance, we obtain the link between maximum and average Lyapunov exponents in line with the previous results. To validate the proposed theoretical results, we present different numerical simulations whose results justify the hypotheses of the present analysis. |
| format | Article |
| id | doaj-art-c6d2e15bc2114272be14a8f0f7f352c7 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-c6d2e15bc2114272be14a8f0f7f352c72025-02-03T06:45:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/23656022365602Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic TurbulenceNicola de Divitiis0“La Sapienza” University, Dipartimento di Ingegneria Meccanica e Aerospaziale, Via Eudossiana, 18, 00184 Rome, ItalyThe present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed chaos, this statistics is here analyzed assuming that the entropy associated with the fluid kinematic state is maximum. The distribution of the local Lyapunov exponents results in an unsymmetrical uniform function in a proper interval of variation. From this PDF, we determine the relationship between average and maximum Lyapunov exponents and the longitudinal velocity correlation function. This link, which in turn leads to the closure of von Kármán–Howarth and Corrsin equations, agrees with results of previous works, supporting the proposed PDF calculation, at least for the purposes of the energy cascade main effect estimation. Furthermore, through the property that the Lyapunov vectors tend to align the direction of the maximum growth rate of trajectories distance, we obtain the link between maximum and average Lyapunov exponents in line with the previous results. To validate the proposed theoretical results, we present different numerical simulations whose results justify the hypotheses of the present analysis.http://dx.doi.org/10.1155/2018/2365602 |
| spellingShingle | Nicola de Divitiis Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence Advances in Mathematical Physics |
| title | Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence |
| title_full | Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence |
| title_fullStr | Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence |
| title_full_unstemmed | Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence |
| title_short | Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence |
| title_sort | statistics of finite scale local lyapunov exponents in fully developed homogeneous isotropic turbulence |
| url | http://dx.doi.org/10.1155/2018/2365602 |
| work_keys_str_mv | AT nicoladedivitiis statisticsoffinitescalelocallyapunovexponentsinfullydevelopedhomogeneousisotropicturbulence |