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Mean flows driven by weak eddies in rotating systems

Published online by Cambridge University Press:  19 April 2006

A. D. Mcewan ,
R. O. R. Y. Thompson  and
R. A. Plumb
A. D. Mcewan
Affiliation:
CSIRO Division of Atmospheric Physics, Aspendale, Victoria, 3195, Australia
R. O. R. Y. Thompson
Affiliation:
CSIRO Division of Atmospheric Physics, Aspendale, Victoria, 3195, Australia Present address: CSIRO Division of Fisheries & Oceanography, Cronulla, N.S.W. 2230, Australia.
R. A. Plumb
Affiliation:
CSIRO Division of Atmospheric Physics, Aspendale, Victoria, 3195, Australia
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Abstract

General relations are derived for the forcing of a mean zonal flow in a damped rotating barotropic system through the action of weak eddies. In particular it is found that if the eddies are forced at localized latitudes the induced motion away from these latitudes is likely to be counter to the rotation (i.e. ‘easterly’). Over the forcing latitude the mean motion is always westerly except when the forcing provides a sink of relative momentum. In the case when the background field is deformed topographically to generate eddies the divergence of the Reynolds stress is balanced at lowest order by a dynamic pressure drag, and the mean motion takes the direction of propagation of the forcing.

The relations are applied to a linearized Rossby wave field in a viscous fluid driven by a moving system of boundary sources and sinks or hills and hollows. The results are compared with laboratory experiments. All major predictions are confirmed qualitatively, but the discrepancies in detail indicate the influence of nonlinear effects other than those incorporated in the theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 3 , 14 August 1980 , pp. 655 - 672
Copyright
© 1980 Cambridge University Press

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References

Andrews, D. G. & McIntyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89, 609–646.Google Scholar
Baines, P. G. & Frederiksen, J. S. 1978 Baroclinic instability on a sphere in two-layer models. Quart. J. Roy. Met. Soc. 104, 45–68.Google Scholar
Blackmon, M. L., Wallace, J. M., Lau, N. & Mullen, S. L. 1977 An observational study of the Northern Hemisphere wintertime circulation. J. Atmos. Sci. 34, 1040–1053.Google Scholar
Colin de Verdière, A. 1977 Quasi-geostrophic flows and turbulence in a rotating homogeneous fluid. Ph.D. thesis, Woods Hole Oceanographic Institution, Massachusetts.
Colin de Verdière, A. 1979 Mean flow generation by topographic Rossby waves. J. Fluid Mech. 94, 39–64.Google Scholar
Frederiksen, J. S. 1979 The effect of long planetary waves on the regions of cyclogenesis: linear theory. J. Atmos. Sci. 36, 195–204.Google Scholar
Held, I. M. 1975 Momentum transport by quasi-geostrophic eddies. J. Atmos. Sci. 32, 1494–1497.Google Scholar
Holopainen, E. O. 1978 On the dynamic forcing of the long-term mean flow by the large-scale Reynolds stresses in the atmosphere. J. Atmos. Sci. 35, 1596–1604.Google Scholar
Hollingsworth, A. 1975 Baroclinic instability of simple flow on a sphere. Quart. J. Roy. Met. Soc. 101, 495–528.Google Scholar
Lorenz, E. N. 1960 Energy and numerical weather prediction. Tellus 12, 364–373.Google Scholar
McIntyre, M. E. 1980 An introduction to the generalised Lagrangian-mean description of wave, mean-flow interaction. Pageoph. 118, 152–176.Google Scholar
Moura, A. D. & Stone, P. H. 1976 The effects of spherical geometry on baroclinic instability. J. Atmos. Sci. 33, 602–616.Google Scholar
Newell, R. E., Kidson, J. W., Vincent, D. G. & Boer, G. J. 1972 The General Circulation of the Tropical Atmosphere and Interactions with Extratropical Latitudes. Massachusetts Institute of Technology Press.
Oort, A. & Rasmussen, E. M. 1971 Atmospheric circulation statistics. N.O.A.A. Prof. Paper 5. U.S. Govt. Printing Office.Google Scholar
Rhines, P. B. 1977 The dynamics of unsteady currents. The Sea, vol. 6 (ed. E. D. Goldberg, I. N. McCave, J. J. O'Brien & J. H. Stelle), pp. 189–318. Wiley.
Rhines, P. B. & Holland, W. R. 1979 A theoretical discussion of eddy-driven mean flows. Dyn. of Atmospheres & Oceans 3, 289–325.Google Scholar
Simmons, A. J. & Hoskins, B. J. 1976 Baroclinic instability on the sphere: normal modes of the primitive and quasi-geostrophic equations. J. Atmos. Sci. 33, 1454–1477.Google Scholar
Starr, V. P. 1968 Physics of Negative Viscosity Phenomena. McGraw-Hill.
Stern, M. E. 1975 Ocean Circulation Physics. Academic.
Taylor, G. I. 1915 Eddy motion in the atmosphere. Phil. Trans. Roy. Soc. A 15, 1–26.Google Scholar
Thompson, R. O. R. Y. 1971 Why there is an intense Eastward current in the North Atlantic, but not in the South Atlantic. J. Phys. Oceanog. 1, 235–237.Google Scholar
Thompson, R. O. R. Y. 1977 Observations of Rossby waves near Site D. Prog. Oceanog. 7, 135–162.Google Scholar
Thompson, R. O. R. Y. 1978 Reynolds stress and deep counter currents near the Gulf Stream. J. Mar. Res. 36, 611–615.Google Scholar
Webster, F. 1965 Measurements of the eddy fluxes of momentum in the surface layer of the Gulf Stream. Tellus 17, 239–245.Google Scholar
Whitehead, J. 1975 Mean flow generated by circulation on a β-plane: an analogy with the moving flame experiment. Tellus 27, 358–364.CrossRefGoogle Scholar