Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T08:58:27.646Z Has data issue: false hasContentIssue false
  • English
  • Français

The ‘Richardson’ criterion for compressible swirling flows

Published online by Cambridge University Press:  29 March 2006

Demetrius P. Lalas
Demetrius P. Lalas
Affiliation:
Department of Mechanical Engineering Sciences, Wayne State University, Detroit, Michigan 48202
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of a compressible non-dissipative swirling flow to adiabatic infinitesimal disturbances of arbitrary orientation is considered. The resulting sufficient condition for stability is the general form of the effective Richardson criterion for swirling flows, first obtained, for axisymmetric modes only, by Howard. In addition, upper bounds to the growth rate of unstable modes are obtained and some extensions of the semicircle theorem to azimuthal disturbances are stated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 1 , 13 May 1975 , pp. 65 - 72
Copyright
© 1975 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

Chimonas, G. 1970 The extension of the Miles-Howard theorem to compressible fluids J. Fluid Mech. 43, 833–836.Google Scholar
Howard, L. N. 1961 Note on a paper of John W. Miles J. Fluid Mech. 10, 509–512.Google Scholar
Howard, L. N. 1973 On the stability of compressible swirling flow Studies in Appl. Math. 52, 39–43.Google Scholar
Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows J. Fluid Mech. 14, 463–476.Google Scholar
Kurzweg, V. H. 1969 A criterion for the stability of heterogeneous swirling flows Z. angew. Math. Phys. 20, 141–143.Google Scholar
Leibovich, S. 1969 Stability of density stratified rotating flows, A.I.A.A. J. 7, 177–178.Google Scholar
Lessen, M., Sadler, S. & Lin, T. 1968 Stability of pipe Poiseuille flow Phys. Fluids, 11, 1404–1409.Google Scholar
Maslowe, S. A. 1974 Instability of rigidly rotating flows to non-axisymmetric disturbances J. Fluid Mech. 64, 307–317.Google Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flows J. Fluid Mech. 10, 496–508.Google Scholar
Pedley, T. J. 1968 On the stability of rapidly rotating shear flows to non-axisymmetric disturbances J. Fluid Mech. 31, 603–607.Google Scholar