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Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-07
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
de Divitiis, Nicola. 2018. Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-12.
https://search.emarefa.net/detail/BIM-1119095
Modern Language Association (MLA)
de Divitiis, Nicola. Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence. Advances in Mathematical Physics No. 2018 (2018), pp.1-12.
https://search.emarefa.net/detail/BIM-1119095
American Medical Association (AMA)
de Divitiis, Nicola. Statistics of Finite Scale Local Lyapunov Exponents in Fully Developed Homogeneous Isotropic Turbulence. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-12.
https://search.emarefa.net/detail/BIM-1119095
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119095