Numerical study of chaos based on a shell model

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number2
Publication statusPublished - Jun 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


Dive into the research topics of 'Numerical study of chaos based on a shell model'. Together they form a unique fingerprint.

Cite this