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Estimation of the turbulent energy production across a shock wave

Published online by Cambridge University Press:  08 February 2006

S. L. GAVRILYUK  and
R. SAUREL
S. L. GAVRILYUK
Affiliation:
Polytech Marseille, UMR CNRS 6595 IUSTI, 5 rue E. Fermi, 13453 Marseille Cedex 13, Francesergey.gavrilyuk@polytech.univ-mrs.fr Laboratoire de Modélisation en Mécanique et Thermodynamique, Faculté des Sciences et Techniques de Saint-Jérôme Case 322, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, Francesergey.gavrilyuk@univ.u-3mrs.fr
R. SAUREL
Affiliation:
Institut Universitaire de France and Polytech Marseille, UMR CNRS 6595 IUSTI, 5 rue E. Fermi, 13453 Marseille Cedex 13, Francerichard.saurel@polytech.univ-mrs.fr
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Abstract

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The simplest model of isotropic compressible turbulence consists of the Euler equations augmented by the equation for the turbulent energy. This model can also be viewed as the Euler equations for a continuum with two independent entropies. One of them is a conventional thermodynamic entropy, and the other is associated with the turbulent energy. The shock relations for this model are examined. It is shown that the turbulent entropy cannot exceed some critical value. We propose a closed set of Rankine–Hugoniot relations for the description of shock waves in such a medium based on this estimation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 549 , 25 February 2006 , pp. 131 - 139
Copyright
© 2006 Cambridge University Press