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A cylindrical sound pulse in a rotating gas

Published online by Cambridge University Press:  28 March 2006

L. E. Fraenkel
L. E. Fraenkel
Affiliation:
Aeronautics Department, Imperial College, London
This work was done while the author was at the Guggenheim Aeronautical Laboratory, California Institute of Technology.
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Abstract

This paper deals with the propagation of a sound pulse into a gas which initially has solid-body rotation and constant temperature, the initial pressure and density increasing outwards like ex, where x is the square of a certain dimensionless radial co-ordinate. The perturbations are due to a source-like disturbance on the axis of symmetry, which begins to act at time t = 0: most attention is paid to source strengths which vary in time like a Dirac pulse or a step function, but the following remarks apply generally.

Immediately behind the wave front the perturbation velocity and temperature decay like e-½x, while the (absolute) perturbation pressure and density grow like e½x (the relative pressure and density increments, which are referred to local conditions in the undisturbed state, then also decay like e-½x). The rotation also introduces oscillations in flows which, with the same disturbance at the origin and no rotation, would vary monotonically with time at a given point.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 5 , Issue 4 , May 1959 , pp. 637 - 649
Copyright
© 1959 Cambridge University Press

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References

Erdélyi, A. (ed.) 1953 Higher Transcendental Functions, Vol. I. New York: McGraw-Hill.
Jahnke, E. & Emde, F. 1945 Tables of Functions, 4th ed. New York: Dover.
Squire, H. B. 1956 Rotating fluids. Article in Surveys in Mechanics, p. 139. Cambridge University Press.
Tricomi, F. G. 1954 Funzioni Ipergeometriche Confluenti. Rome: Edizioni Cremonese.
Whitham, G. B. 1952 The flow pattern of a supersonic projectile. Comm. Pure Appl. Math. 5, 30.Google Scholar