Validity of the essential assumption in a projection operator method

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Abstract

The projection operator method developed by Mori involves the essential assumption that chaotic motion is successfully divided into a coherent motion and a fluctuating one. We investigate the validity of the assumption using the Kuramoto-Sivashinsky equation as a model equation of chaotic systems. It has been found that the assumption is reasonable for both long wave modes and short wave modes. We have also evaluated a value of the eddy viscosity as 9.0 by extracting the nonlinear term from the coherent part. This value is consistent with the former estimates with other methods.

Original languageEnglish
Article number046210
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number4
DOIs
Publication statusPublished - Oct 23 2006

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Projection Operator
projection
operators
Kuramoto-Sivashinsky Equation
Eddy Viscosity
eddy viscosity
Chaotic Motion
planetary waves
Chaotic System
Motion
Term
estimates
Estimate
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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abstract = "The projection operator method developed by Mori involves the essential assumption that chaotic motion is successfully divided into a coherent motion and a fluctuating one. We investigate the validity of the assumption using the Kuramoto-Sivashinsky equation as a model equation of chaotic systems. It has been found that the assumption is reasonable for both long wave modes and short wave modes. We have also evaluated a value of the eddy viscosity as 9.0 by extracting the nonlinear term from the coherent part. This value is consistent with the former estimates with other methods.",
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AB - The projection operator method developed by Mori involves the essential assumption that chaotic motion is successfully divided into a coherent motion and a fluctuating one. We investigate the validity of the assumption using the Kuramoto-Sivashinsky equation as a model equation of chaotic systems. It has been found that the assumption is reasonable for both long wave modes and short wave modes. We have also evaluated a value of the eddy viscosity as 9.0 by extracting the nonlinear term from the coherent part. This value is consistent with the former estimates with other methods.

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