Article contents
The ‘Richardson’ criterion for compressible swirling flows
Published online by Cambridge University Press: 29 March 2006
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
- Copyright
- © 1975 Cambridge University Press
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.
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
- 25
- Cited by