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Local baroclinic instability of flow over variable topography

Published online by Cambridge University Press:  26 April 2006

R. M. Samelson  and
J. Pedlosky
R. M. Samelson
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
J. Pedlosky
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
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Abstract

Local baroclinic instability is studied in a two-layer quasi-geostrophic model. Variable meridional bottom slope controls the local supercriticality of a uniform zonal flow. Solutions are found by matching pressure, velocity, and upper-layer vorticity across longitudes where the bottom slope changes abruptly so as to destabilize the flow in a central interval of limited zonal extent. In contrast to previous results from heuristic models, an infinite number of modes exist for arbitrarily short intervals. For long intervals, modal growth rates and frequencies approach the numerical and WKB results for the most unstable mode. For intervals of length comparable to and smaller than the wavelengths of unstable waves in the homogeneous problem, the WKB results lose accuracy. The modes retain large growth rates (about half maximum) for intervals as short as the internal deformation radius. Evidently, the deformation radius and not the homogeneous instability determines the fundamental scale for local instability. Maximum amplitudes occur near the downstream edge of the unstable interval. Lower-layer amplitudes decay downstream more rapidly than upper-layer amplitudes. For short intervals, the instability couples motions with widely disparate horizontal scales in the upper and lower layers. Heat flux is more strictly confined than amplitude. Growth rates increase linearly with weak supercriticality.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 411 - 436
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
Eady, E. T.: 1949 Long waves and cyclone waves. Tellus 1, 33–52.Google Scholar
Frederiksen, J. S.: 1983 Disturbances and eddy fluxes in northern hemisphere flows: Instability of three dimensional January and July flows. J. Atmos. Sci. 40, 836–855.Google Scholar
Gent, P. R. & Leach, H., 1976 Baroclinic instability in an eccentric annulus. J. Fluid Mech. 77, 769–788.Google Scholar
Holopainen, E. O.: 1983 Transient eddies in mid-latitudes: Observations and interpretation. In Large-Scale Dynamical Processes in the Atmosphere (ed. B. Hoskins & R. Pearce), chap. 8. Academic.
Merkine, L. & Shafranek, M., 1980 The spatial and temporal evolution of localized unstable baroclinic disturbances. Geophys. Astrophys. Fluid Dyn. 16, 174–206.Google Scholar
Pedlosky, J.: 1979 Geophy. Fluid Dyn. Springer, 624 pp.
Pedlosky, J.: 1989 Simple models for local instabilities in zonally inhomogeneous flows. J. Atmos. Sci. 46, 1769–1778.Google Scholar
Phillips, N. A.: 1954 Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level quasi-geostrophic model. Tellus 6, 273–286.Google Scholar
Pierrehumbert, R.: 1984 Local and global baroclinic instability of zonally varying flow. J. Atmos. Sci. 41, 2141–2162.Google Scholar