Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T07:51:22.860Z Has data issue: false hasContentIssue false
  • English
  • Français

Waves in a gas in solid-body rotation

Published online by Cambridge University Press:  29 March 2006

J. B. Morton  and
E. J. Shaughnessy
J. B. Morton
Affiliation:
Department of Aerospace Engineering and Engineering Physics, University of Virginia, Charlottesville
E. J. Shaughnessy
Affiliation:
Department of Aerospace Engineering and Engineering Physics, University of Virginia, Charlottesville
Get access Rights & Permissions [Opens in a new window]

Abstract

The axial and transverse wave motions of an inviscid perfect gas in isothermal solid-body rotation in a cylinder are investigated. Solutions of the resulting eigenvalue problem are shown to correspond to two types of waves. The acoustic waves are the rotational counterparts of the well-known Rayleigh solutions for a gas at rest in a cylinder. The rotational waves, whose amplitudes and frequencies go to zero in the non-rotating limit, exhibit phase speeds both larger and smaller than the speed of sound. The effect of rotation on the frequency and structure of these waves is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 2 , 28 November 1972 , pp. 277 - 286
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1968 Handbook of Mathematical Functions. Washington: U.S. Government Printing Office.
Fraenkel, L. E. 1959 J. Fluid Mech. 5, 637–649.
Greenspan, H. P. 1968 The Theory of Rotating fluids. Cambridge University Press.
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.
Maslen, S. H. & Moore, F. K. 1956 J. Aero Sci. 23, 583.
Rayleigh, Lord1896 The Theory of Sound, 2nd edn. Dover.
Salant, R. F. 1968 J. Acoust. Soc. Am. 43, 1302–1305.
Slater, L. J. 1960 Confluent Hypergeametric Functions. Cambridge University Press.
Sozou, C. 1969a J. Acoust. Soc. Am. 46, 814–818.
Sozou, C. 1969b J. Fluid Mech. 36, 605–612.
Sozou, C. & Swithenbank, J. 1969 J. Fluid Mech. 38, 657–671.