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Conical flow near singular rays

Published online by Cambridge University Press:  29 March 2006

G. I. Zahalak  and
M. K. Myers
G. I. Zahalak
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University Present address: Brown University.
M. K. Myers
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University Present address: Joint Institute for Acoustics and Flight Sciences, The George Washington University.
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Abstract

The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 3 , 29 April 1974 , pp. 537 - 561
Copyright
© 1974 Cambridge University Press

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References

Bagdoyev, A. G. 1969 Nonlinear Problems of Compressible Flow. Jerusalem: Israel Programme for Scientific Translations.
Courant, R. & Friedrichs, K. O. 1967 Supersonic Plow and Shock Waves. Interscience.
Courant, R. & Hilbert, D. 1966 Methods of Mathematical Physics, vol.2. Interscience.
Davis, S. S. 1969 Ph.D. thesis, Columbia University.
Davis, S. B. 1971 Third Conf. onSonic Boom Rea., N.A.S.A. Special Publ. no. 255, 219.
Erdélyi, A. 1956 Asymptotic Expansions. Dover.
Hayes, W. D. 1971 Third Conf. on Sonic Boom Res., N.A.S.A. Special Publ. no.255, 405.
Hayes, W. D. et al. 1971 Third Conf. on Sonic Boom Res., N.A.S.A. Special Publ. no.255, 27.
Keller, J. B. 1954 J. Appl. Phys. 25, 938.
Kuo, Y. H. 1955 J. Aero. Sci. 22, 504.
Legras, J. 1953 Onerapubl. no.66.
Lighthill, M. J. 1949a Phil. Mag. 40 (7), 1179.
Lighthill, M. J. 1949b Phil. Mag. 40 (7), 1202.
Myers, M. K. 1971 Third Conf. on Sonic Boom Res., N.A.X.A. Special Publ. no. 255, 75.
Seebass, R. 1971 Third Conf. on Sonic BoomRes., N.A.S.A. Special Publ. no. 255, 87.
VAN Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Ward, G. N. 1955 Linearized Theory of Steady High-speed Flow. Cambridge University Press.
Whitham, G. B. 1952 Comm. Pure Appl. Maths. 5, 301.
Whitham, G. B. 1956 J. Fluid Mech. 1, 290.
Zahalak, G. I. 1972 Ph.D. thesis, Columbia University.