Comparison Analysis of Lorenz Model and Five Components Model

Takashi Aoyagi, Masatoshi Yagi, Sanae Itoh

Research output: Contribution to journalReview article

3 Citations (Scopus)

Abstract

The Lorenz model for Rayleigh-Bénard convection is extended to the five components model taking an autonomous shear flow effect into account. The five components model is numerically solved and analyzed in detail. Based on the Lyapunov exponent analysis , how the introduction of the new degrees of the freedom (the shear flow) changes the chaotic behavior of the solution is examined. The attractors, the time evolutions, the power spectra, the Nusselt number of the five components model are compared with those of the Lorenz model. It is found that the solutions of both models converge to the same one when the Rayleigh number is small. When the Rayleigh number exceeds a critical value, the difference between the Lorenz model and the five components model is observed, i.e., the former has only the periodic solutions, while the latter contains the chaotic solutions. Some examples are shown. The limitation to a model with a few degrees of freedom is also discussed.

Original languageEnglish
Pages (from-to)2689-2701
Number of pages13
JournalJournal of the Physical Society of Japan
Volume66
Issue number9
DOIs
Publication statusPublished - Jan 1 1997

Fingerprint

Rayleigh number
shear flow
Nusselt number
power spectra
convection
degrees of freedom
exponents

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Comparison Analysis of Lorenz Model and Five Components Model. / Aoyagi, Takashi; Yagi, Masatoshi; Itoh, Sanae.

In: Journal of the Physical Society of Japan, Vol. 66, No. 9, 01.01.1997, p. 2689-2701.

Research output: Contribution to journalReview article

Aoyagi, Takashi ; Yagi, Masatoshi ; Itoh, Sanae. / Comparison Analysis of Lorenz Model and Five Components Model. In: Journal of the Physical Society of Japan. 1997 ; Vol. 66, No. 9. pp. 2689-2701.
@article{c9563b44a82a42a3a60f477bafca9c55,
title = "Comparison Analysis of Lorenz Model and Five Components Model",
abstract = "The Lorenz model for Rayleigh-B{\'e}nard convection is extended to the five components model taking an autonomous shear flow effect into account. The five components model is numerically solved and analyzed in detail. Based on the Lyapunov exponent analysis , how the introduction of the new degrees of the freedom (the shear flow) changes the chaotic behavior of the solution is examined. The attractors, the time evolutions, the power spectra, the Nusselt number of the five components model are compared with those of the Lorenz model. It is found that the solutions of both models converge to the same one when the Rayleigh number is small. When the Rayleigh number exceeds a critical value, the difference between the Lorenz model and the five components model is observed, i.e., the former has only the periodic solutions, while the latter contains the chaotic solutions. Some examples are shown. The limitation to a model with a few degrees of freedom is also discussed.",
author = "Takashi Aoyagi and Masatoshi Yagi and Sanae Itoh",
year = "1997",
month = "1",
day = "1",
doi = "10.1143/JPSJ.66.2689",
language = "English",
volume = "66",
pages = "2689--2701",
journal = "Journal of the Physical Society of Japan",
issn = "0031-9015",
publisher = "Physical Society of Japan",
number = "9",

}

TY - JOUR

T1 - Comparison Analysis of Lorenz Model and Five Components Model

AU - Aoyagi, Takashi

AU - Yagi, Masatoshi

AU - Itoh, Sanae

PY - 1997/1/1

Y1 - 1997/1/1

N2 - The Lorenz model for Rayleigh-Bénard convection is extended to the five components model taking an autonomous shear flow effect into account. The five components model is numerically solved and analyzed in detail. Based on the Lyapunov exponent analysis , how the introduction of the new degrees of the freedom (the shear flow) changes the chaotic behavior of the solution is examined. The attractors, the time evolutions, the power spectra, the Nusselt number of the five components model are compared with those of the Lorenz model. It is found that the solutions of both models converge to the same one when the Rayleigh number is small. When the Rayleigh number exceeds a critical value, the difference between the Lorenz model and the five components model is observed, i.e., the former has only the periodic solutions, while the latter contains the chaotic solutions. Some examples are shown. The limitation to a model with a few degrees of freedom is also discussed.

AB - The Lorenz model for Rayleigh-Bénard convection is extended to the five components model taking an autonomous shear flow effect into account. The five components model is numerically solved and analyzed in detail. Based on the Lyapunov exponent analysis , how the introduction of the new degrees of the freedom (the shear flow) changes the chaotic behavior of the solution is examined. The attractors, the time evolutions, the power spectra, the Nusselt number of the five components model are compared with those of the Lorenz model. It is found that the solutions of both models converge to the same one when the Rayleigh number is small. When the Rayleigh number exceeds a critical value, the difference between the Lorenz model and the five components model is observed, i.e., the former has only the periodic solutions, while the latter contains the chaotic solutions. Some examples are shown. The limitation to a model with a few degrees of freedom is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0031521753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031521753&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.66.2689

DO - 10.1143/JPSJ.66.2689

M3 - Review article

VL - 66

SP - 2689

EP - 2701

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 9

ER -