Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A hodograph approach to the rotational compressible flow of an ideal fluid


Author: Gianfranco Chiocchia
Journal: Quart. Appl. Math. 47 (1989), 513-528
MSC: Primary 76M05; Secondary 76H05, 76N10
DOI: https://doi.org/10.1090/qam/1012274
MathSciNet review: MR1012274
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Abstract: The classical hodograph equation for the study of the irrotational compressible flow of an ideal gas is here extended to the rotational case in which an entropy gradient normal to the streamlines is present. The formulation is in terms of Crocco's stream function and leads to an equation differing from that valid for the irrotational case because of an additional nonlinear te[ill]m. In spite of this nonlinearity an exact solution can be found, describing a class of rotational vortices. Moreover, perturbative solutions can be found for the case in which the entropy gradient and the vorticity are small: one of these is here presented and describes the superposition of a constant vorticity distribution to the transonic region of the Ringleb flow.


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DOI: https://doi.org/10.1090/qam/1012274
Article copyright: © Copyright 1989 American Mathematical Society


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