Study of self-similar and steady flows near singularities

Bhatnagar, P. L. ; Prasad, Phoolan (1970) Study of self-similar and steady flows near singularities Proceedings of the Royal Society of London Series A: Mathematical, Physical & Engineering Sciences, 315 (1523). pp. 569-584. ISSN 0962-8444

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One-dimensional steady state flow or a self-similar flow is represented by an integral curve of the system of ordinary differential equations and, in many important cases, the integral curve passes through a singular point. Kulikovskii & Slobodkina (1967) have shown that the stability of a steady flow near the singularity can be studied with the help of a simple first-order partial differential equation. In section 2 of this paper we have used their method to study steady transonic flows in radiation-gas-dynamics in the neighbourhood of the sonic point. We find that all possible one-dimensional steady flows in radiation-gas-dynamics are locally stable in the neighbourhood of the sonic point. A continuous disturbance on a steady flow, while decaying and propagating, may develop a surface of discontinuity within it. We have determined the conditions for the appearance of such a discontinuity and also the exact position where it appears. In section 3 we have shown that their method can be easily generalized to study the stability of self-similar flows. As an example we have considered the stability of the self-similar flow behind a strong imploding shock. In this case we find that the flow is stable with respect to radially symmetric disturbances.

Item Type:Article
Source:Copyright of this article belongs to Royal Society Publishing.
ID Code:4960
Deposited On:18 Oct 2010 08:32
Last Modified:16 May 2016 15:32

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