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Baroclinic stability under non-hydrostatic conditions

Published online by Cambridge University Press:  29 March 2006

Peter H. Stone
Peter H. Stone
Affiliation:
Division of Engineering and Applied Physics, Harvard University
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Abstract

Eady's model for the stability of a thermal wind in an inviscid, stratified, rotating system is modified to allow for deviations from hydrostatic equilibrium. The stability properties of the flow are uniquely determined by two parameters: the Richardson number Ri, and the ratio of the aspect ratio to the Rossby number δ. The latter parameter may be taken as a measure of the deviations from hydrostatic equilibrium (δ = 0 in Eady's model). It is found that such deviations decrease the growth rates of all three kinds of instability which can occur in this problem: ‘geostrophic’ baroclinic instability, symmetric instability, and Kelvin–Helmholtz instability. The unstable wavelengths for ‘geostrophic’ and Kelvin–Helmholtz instability are increased for finite values of δ, while the unstable wavelengths for symmetric instability are unaffected. The ‘non-hydrostatic’ effects (δ ≠ 0) are significant for symmetric and Kelvin–Helmholtz instability when δ [gsim ] 1, but not for ‘geostrophic’ instability unless δ [Gt ] 1. Consequently, the first two types of instability tend to be suppressed relative to ‘geostrophic’ instability by ‘non-hydrostatic’ conditions. Figure 3 summarizes the different instability régimes that can occur. In laboratory experiments symmetric instability can be studied best when δ [lsim ] 1, while Kelvin–Helmholtz instability can be studied best when δ [Lt ] 1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 4 , 26 February 1971 , pp. 659 - 671
Copyright
© 1971 Cambridge University Press

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References

Charney, J. G. 1947 The dynamics of long waves in a baroclinic westerly current J. Meteor. 4, 135–162.Google Scholar
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of inviscid fluid Advanc. appl. Mech. 9, 1–89.Google Scholar
Eady, E. T. 1949 Long waves and cyclone waves Tellus, 1, 33–52.Google Scholar
Eliassen, A., Hoiland, E. & Riis, E. 1953 Two-dimensional perturbation of a flow with constant shear of a stratified fluid. Publications of the Norwegian Academy of Sciences and Letters (Series W), no. 1, 30 pp.
Fowlis, W. W. & Hide, R. 1965 Thermal convection in a rotating annulus J. Atmos. Sci. 22, 541–558.Google Scholar
Fultz, D., Long, R. R., Owens, G. V., Bohan, W., Kaylor, R. & Weil, J. 1959 Studies of thermal convection in a rotating cylinder Meteor. Monogr. 4, 1–104.Google Scholar
McIntyre, M. E. 1969 Diffusive destabilization of the baroclinic circular vortex Geophysical Fluid Dynamics, 1, 19–58.Google Scholar
Phillips, N. A. 1963 Geostrophic motion Rev. Geophys. 1, 123–176.Google Scholar
Solberg, H. 1936 Le Mouvement d'Inertie de l'Atmosphère Stable et son Rôle dans la Théorie des Cyclones. Proc.-verb. Assc. Météor. U.G.G.I. (Edinburgh), part II (Mém.), pp. 66–82.
Stone, P. H. 1966 On non-geostrophic baroclinic stability J. atmos. Sci. 23, 390–400.Google Scholar
Stone, P. H. 1970 On non-geostrophic baroclinic stability. Part II. J. atmos. Sci. 27. (To be published.)Google Scholar
Stone, P. H., Hess, S., Hadlock, R. & Ray, P. 1969 Preliminary results of experiments with symmetric baroclinic instabilities J. atmos. Sci. 26, 991–996.Google Scholar