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A note on the stability of steady inviscid helical gas flows

Published online by Cambridge University Press:  19 April 2006

Knut S. Eckhoff
Affiliation:
Department of Mathematics, Allégt. 53-55, 5014 Bergen-Universitetet, Norway
Leiv Storesletten
Affiliation:
Department of Mathematics, Agder Regional College, Boks 607, 4601 Kristiansand, Norway

Abstract

A necessary condition for linear stability of steady inviscid helical gas flows is found by the generalized progressing-wave expansion method. The criterion obtained is compared with the known Richardson number criteria giving sufficient conditions for stability.

Type
Research Article
Copyright
© 1978 Cambridge University Press

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References

Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics, vol. 2. Interscience.
Eckart, C. 1960 Hydrodynamics of Oceans and Atmospheres. Pergamon.
Eckhoff, K. S. 1975 Stability problems for linear hyperbolic systems. Dept. Appl. Math., Univ. Bergen, Rep. no. 54.Google Scholar
Friedlander, F. G. 1958 Sound Pulses. Cambridge University Press.
Gans, R. F. 1975 On the stability of shear flow in a rotating gas. J. Fluid Mech. 68, 403412.Google Scholar
Howard, L. N. 1973 On the stability of compressible swirling flow. Stud. Appl. Math. 52, 3943.Google Scholar
Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14, 463476.Google Scholar
Ludwig, D. 1960 Exact and asymptotic solutions of the Cauchy problem. Comm. Pure Appl. Math. 13, 473508.Google Scholar
Roseau, M. 1966 Vibrations Non Linéaires et Théorie de la Stabilité. Springer.
Warren, F. W. 1975 A comment on Gans’ stability criterion for steady inviscid helical gas flows. J. Fluid Mech. 68, 413415.Google Scholar
Yih, C.-S. 1965 Dynamics of Non-homogeneous Fluids. Macmillan.