Invariant Manifolds in Parametric turbulent Models

• Grebenev, Vladimir N ^[1] ; Chernykh, G. G. ^[1]
  1. [1] Institute of Computational Technologies

     Institute of Computational Technologies

     Rusia

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 11, Nº. 2, 2004, págs. 1-23
• Idioma: inglés
• DOI: 10.15517/rmta.v11i2.240
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• Resumen
  • español

    El artículo trata de examinar el llamado equilibrio local de aproximaciones usado cuando se modelan fluidos turbulentos. La dinámica de una estela turbulenta plana es estudiada como un ejemplo. Analizamos estas aproximaciones usando el método de restricciones diferenciales. Mostramos que algunos modelos algebraicos basados en el uso de la aproximación de equilibrio local pueden ser interpretadas como ecuaciones de variedades invariantes generadas por los modelos bajo consideración. La reducción de los modelos a las variedades correspondientes hicieron posible encontrar soluciones auto-similares y separar soluciones explícitas. Es más, algunas constantes empíricas pueden ser calculadas y los valores obtenidos son cercanos a las cantidades recomendadas.

  • English

    The article is devoted to examining the so-called local-equilibrium approximations used while modeling turbulent flows. The dynamics of a far plane turbulent wake are investigated as an example. In this article, we analyze these approximations by using the method of differential constraints. We show that some algebraic models based on using the local-equilibrium approximation can be interpreted as equations of invariant manifolds generated by the models under consideration. Reduction of the models on the corresponding invariant manifolds made it possible to find self similar solutions and to separate explicit solutions. Moreover, some empirical constants may be calculated and their obtained values are close to the recommended quantities.

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