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On the evaluation of barotropic-baroclinic instability parameters of zonal flows on a beta-plane

Published online by Cambridge University Press:  26 April 2006

Vladimir G. Gnevyshev  and
Victor I. Shrira
Vladimir G. Gnevyshev
Affiliation:
P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences, Krasikova 23, Moscow 117218, USSR
Victor I. Shrira
Affiliation:
P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences, Krasikova 23, Moscow 117218, USSR
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Abstract

The paper is concerned with the problem of the linear stability of an arbitrary inviscid zonal flow on a β-plane. Based on the analysis of integral relations following from the linear boundary-value problem, new evaluations, considerably more exact than the previously known ones, of the parameter region of unstable disturbances are derived. Some new relations among these bounds are established.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 161 - 181
Copyright
© 1990 Cambridge University Press

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References

Charney, J. G.: 1947 The dynamics of long waves in a baroclinic westerly current. J. Met. 4, 135–162.Google Scholar
Drazin, P. G. & Reid, W. H., 1981 Hydrodynamic Stability. Cambridge University Press.
Gnevyshev, V. G. & Shrira, V. I., 1990 On the stability of geophysical flows with Rayleigh viscosity. Izv. Akad. Nauk. SSSR Atmos. Ocean. Phys. (submitted).Google Scholar
Hall, R. E.: 1980 A note on a semicircle theorem. Dyn. Atmos. Oceans 5, 113–121.Google Scholar
Howard, L. N.: 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509–512.Google Scholar
Killworth, P. D.: 1980 Barotropic and baroclinic instability in rotating stratified fluid. Dyn. Atmos. Oceans 4, 143–184.Google Scholar
Kochar, G. T. & Jain, R. K., 1979 Note on Howard's semicircle theorem. J. Fluid Mech. 91, 489–491.Google Scholar
Makov, Yu. N. & Stepanyants, Yu. A., 1984 Note on the paper of Kochar and Jain on Howard's semicircle theorem. J. Fluid Mech. 140, 1–10.Google Scholar
Miles, J. M.: 1964 Baroclinic instability of the zonal wind. Rev. Geophys. 2, 155–176.Google Scholar
Pedlosky, J.: 1964 The stability of currents in the atmosphere and the ocean. J. Atmos. Sci. 21, 201–219.Google Scholar
Pedlosky, J.: 1979 Geophysical Fluid Dynamics.
Rayleigh, Lord: 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 9, 57–70.Google Scholar
Romanova, N. N.: 1987 Explosive instability of Rossby waves in three-layered model. Izv. Akad. Sci. SSSR, Atmos. Ocean. Phys. 23, 269–274.Google Scholar