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Baroclinic instability over wavy topography

Published online by Cambridge University Press:  20 April 2006

R. A. De Szoeke
R. A. De Szoeke
Affiliation:
School of Oceanography, Oregon State University, Corvallis, OR 97331
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Abstract

The occurrence of new unstable modes of quasigeostrophic baroclinic oscillation of rotating stratified shear flow over a wavy bottom is examined. To obtain a tractable mathematical problem, the bottom topography is considered as a perturbation modifying the oscillations. It is found that combinations of a top-intensified and a bottom-intensified Eady mode, each stable without topography, can be destabilized by topography if certain resonant conditions are met. These are that (i) the two modes possess the same wavefrequency, and (ii) topography possesses a wavenumber c bridging the gap between the wavenumbers of the modes a, b, i.e. c = a – b. Growth rate of this instability (called type A) is proportional to the amplitude of the topographic component. There are two special cases: (i) when one of the basic modes is a marginally neutral mode – according to the classical analysis without topography – the instability is stronger (type M) with growth rate proportional to the 2/3-power of topographic amplitude; (ii) when both modes are marginally neutral the instability is even stronger (type M2) with growth rate proportional to the square root of topographic amplitude.

These topographic instabilities, like classical baroclinic instability, draw their energy from the available potential by transporting buoyancy down the mean gradient associated with the geostrophic shear flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 279 - 298
Copyright
© 1983 Cambridge University Press

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References

Blumsack, S. L. & Gierasch, P. J. 1972 Mars: the effect of topography on baroclinic instability. J. Atmos. Sci. 29, 1081–1089.Google Scholar
Bretherton, F. P. 1966 Critical layer instability in baroclinic flows Q. J. R. Met. Soc. 92, 325–334.Google Scholar
Charney, J. G. 1947 The dynamics of long waves in a baroclinic westerly current J. Met. 4, 135–163.Google Scholar
Charney, J. G. & Straus, D. M. 1980 Form-drag instability, multiple equilibria and propagating planetary waves in baroclinic, orographically forced, planetary wave systems J. Atmos. Sci. 37, 1157–1176.Google Scholar
Eady, E. T. 1949 Long waves and cyclone waves Tellus 1, 33–52.Google Scholar
Hide, R. & Mason, P. J. 1975 Sloping convection in a rotating fluid Adv. Phys. 24, 47–100.Google Scholar
Mcintyre, M. E. 1970 On the non-separable baroclinic parallel-flow instability problem J. Fluid Mech. 40, 273–306.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Pedlosky, J. 1981 Resonant topographic waves in barotropic and baroclinic flows J. Atmos. Sci. 38, 2626–2641.Google Scholar
Szoeke, R. A. De 1975 Some effects of bottom topography on baroclinic stability J. Mar. Res. 33, 93–122.Google Scholar