Numerical study of chaos based on a shell model

M. Yagi, S. I. Itoh, K. Itoh, A. Fukuyama

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A shell model is introduced to study a turbulence driven by the thermal instability (Rayleigh-Bénard convection). This model equation describes cascade and chaos in the strong turbulence with high Rayleigh number. The chaos is numerically studied based on this model. The characteristics of the turbulence are analyzed and compared with those of the Gledzer-Ohkitani-Yamada (GOY) model. Quantities such as a mean value of total fluctuation energy, it's standard deviation, time averaged wave spectrum, probability distribution function, frequency spectrum, the maximum instantaneous Lyapunov exponent, distribution of instantaneous Lyapunov exponents, are evaluated. The dependences of these quantities on the error of numerical integration are also examined. There is not a clear correlation between the numerical accuracy and the accuracy of these quantities, since the interaction between a truncation error and an intrinsic nonlinearity of the system exists. A finding is that the maximum Lyapunov exponent is insensitive to a truncation error.

Original languageEnglish
Pages (from-to)393-402
Number of pages10
JournalChaos
Volume9
Issue number2
DOIs
Publication statusPublished - Jun 1999

Fingerprint

Shell Model
Chaos theory
Lyapunov Exponent
chaos
Numerical Study
Turbulence
Chaos
Truncation Error
truncation errors
Instantaneous
turbulence
exponents
Numerical Accuracy
Frequency Spectrum
Probability Distribution Function
Rayleigh number
Rayleigh
Mean Value
Standard deviation
Numerical integration

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Yagi, M., Itoh, S. I., Itoh, K., & Fukuyama, A. (1999). Numerical study of chaos based on a shell model. Chaos, 9(2), 393-402. https://doi.org/10.1063/1.166416

Numerical study of chaos based on a shell model. / Yagi, M.; Itoh, S. I.; Itoh, K.; Fukuyama, A.

In: Chaos, Vol. 9, No. 2, 06.1999, p. 393-402.

Research output: Contribution to journalArticle

Yagi, M, Itoh, SI, Itoh, K & Fukuyama, A 1999, 'Numerical study of chaos based on a shell model', Chaos, vol. 9, no. 2, pp. 393-402. https://doi.org/10.1063/1.166416
Yagi M, Itoh SI, Itoh K, Fukuyama A. Numerical study of chaos based on a shell model. Chaos. 1999 Jun;9(2):393-402. https://doi.org/10.1063/1.166416
Yagi, M. ; Itoh, S. I. ; Itoh, K. ; Fukuyama, A. / Numerical study of chaos based on a shell model. In: Chaos. 1999 ; Vol. 9, No. 2. pp. 393-402.
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