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Two hidden symmetries of the equations of ideal gasdynamics, and the general solution in a case of non-uniform entropy distribution

Published online by Cambridge University Press:  20 April 2006

B. Gaffet
B. Gaffet
Affiliation:
Section d'Astrophysique, Centre d'Etudes Nucléaires de Saclay, 91191 Gif-sur-Yvette, France and Department of Astronomy, Kyoto University, Japan
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Abstract

Through an extension of the concept of scale invariance we construct two invariance transformations of the equations of gasdynamics: the first is a true Bäcklund transformation, and as such we expect that it should play an important role in the search for new cases of integrability; the other one affects the shape of the entropy profile, implying that the mathematical problems of isentropic and non-isentropic flow are, at least in some cases, equivalent.

That property enables us to deduce the general solution in closed form, assuming a power-law entropy profile of the form P/ργ ≈ 1/M3γ−1, where M is the Lagrangian mass coordinate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 134 , September 1983 , pp. 179 - 194
Copyright
© 1983 Cambridge University Press

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