The correlation dimension of an attractor determined on the base of the theory of equivalence of measures and stochastic equations for continuum
| Autor: | Artur V. Dmitrenko |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Correlation dimension
Turbulence Stochastic process Mathematical analysis General Physics and Astronomy 02 engineering and technology 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics Boundary layer 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials 0103 physical sciences Attractor General Materials Science Equivalence (measure theory) Hydrodynamic flow Physical law Mathematics |
| Zdroj: | Continuum Mechanics and Thermodynamics. 32:63-74 |
| ISSN: | 1432-0959 0935-1175 |
| Popis: | The physical law of the equivalence of measures between the random process and the regular process and the stochastic equations of continuum have opened the new way in stochastic theory of turbulence. An experimental method for determining the dimension of an attractor for hydrodynamic flows suggests re-conducting an enormous complex of experiments for flows for which data on the measurement of statistical moments have already been obtained. This article proposes the dependence for the calculation of the dimensions of the attractor based on statistical moments. In addition, applying this formula and the results obtained in the stochastic theory of turbulence based on the theory of the equivalence of measures, the new dependence for the dimension of the attractor as a function of initial perturbations in a hydrodynamic flow is presented. Calculated portraits of the correlation dimension of the attractor in the cross section of a circular pipe and in the cross section of the boundary layer on a flat plate are presented. |
| Databáze: | OpenAIRE |
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