Body Force Circulations in a Compressible Atmosphere: Key Concepts

  • Timothy J. Dunkerton
Part of the Pageoph Topical Volumes book series (PTV)


The body force circulation problem of Eliassen is extended to spherical geometry and a quasi-compressible atmosphere using the zonally symmetric tidal theory. The concept of body force circulation is generalized to include the effects of mechanical friction and Newtonian cooling. This viewpoint is conceptually advantageous when the circulation is driven by body forces against radiative relaxation. The resulting linear theory is qualitatively useful in middle atmosphere applications, including the equatorial momentum source for which an analytic solution has not been given previously. Further generalizations of the theory are possible by including dynamical and photochemical feedback effects.

Key words

Mean meridional circulation zonally symmetric tidal theory 


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  1. Abramowitz, M., and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington D.C. 1970) 1046 pp.Google Scholar
  2. Andrews, D. G., and M. E. McIntyre (1976), Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sci. 33, 2031–2048.CrossRefGoogle Scholar
  3. Boyd, J. P., and Z. D. Christidis (1982), Low wavenumber instability on the equatorial beta-plane, Geophys. Res. Lett., 9, 769–772.CrossRefGoogle Scholar
  4. Delisi, D. P., and T. J. Dunkerton (1988), Seasonal variation of the semiannual oscillaton, J. Atmos. Sci.,1 14 to appear.Google Scholar
  5. Dickinson, R. E. (1968), On the excitation and propagation of zonal winds in an atmosphere with Newtonian cooling, J. Atmos. Sci. 25, 269–279.CrossRefGoogle Scholar
  6. Dunkerton, T. J. (1978), On the mean meridional mass motions of the stratosphere and mesosphere, J. Atmos. Sci. 35, 2325–2333.CrossRefGoogle Scholar
  7. Dunkerton, T. J. (1980), A Lagrangian mean theory of wave, mean-flow interaction with applications to nonacceleration and its breakdown, Rev. Geophys. Space Phys. 18, 387–400.CrossRefGoogle Scholar
  8. Dunkerton, T. J. (1981), On the inertial stability of the equatorial middle atmosphere, J. Atmos. Sci. 38, 2354–2364.CrossRefGoogle Scholar
  9. Dunkerton, T. J. (1983), A nonsymmetric equatorial inertial instability, J. Atmos. Sci. 40, 807–813.CrossRefGoogle Scholar
  10. Dunkerton, T. J. (1985), A two-dimensional model of the quasi-biennial oscillation, J. Atmos. Sci. 42, 1151–1160.CrossRefGoogle Scholar
  11. Dunkerton, T. J. (1988), Body force circulation and the Antarctic ozone minimum, J. Atmos. Sci. 45, 427–438.CrossRefGoogle Scholar
  12. Dunkerton, T. J. (1989), Nonlinear Hadley circulation driven by asymmetric differential heating. J. Atmos. Sci., to appear.Google Scholar
  13. Dunkerton, T. J., C.-P. F. Hsu, and M. E. McIntyre (1981), Some Eulerian and Lagrangian diagnostics for a model stratospheric warming, J. Atmos. Sci. 38, 819–843.CrossRefGoogle Scholar
  14. Edmon, H. J., B. J. Hoskins, and M. E. McIntyre (1980), Eliassen-Palm cross sections for the troposphere, J. Atmos. Sci. 37, 2600–2616.CrossRefGoogle Scholar
  15. Eliassen, A. (1951), Slow thermally or frictionally controlled meridional criculation in a circular vortex, Astrophys. Norv.5, 19–60.Google Scholar
  16. Flattery, T. W. (1967), Hough Functions, Technical Report No. 21, Dept. of Geophysical Sciences, University of Chicago, 175 pp.Google Scholar
  17. Garcia, R. R. (1987), On the mean meridional circulation of the middle atmosphere, J. Atmos. Sci. 44, 3599–3609.CrossRefGoogle Scholar
  18. Held, I. M., and A. Y. Hou (1980), Nonlinear axially symmetric circulations in a nearly inviscid atmosphere, J. Atmos. Sci. 37, 515–533.CrossRefGoogle Scholar
  19. Holl, P. (1979), The completeness of the orthogonal system of the Hough functions. Translated by B. Haurwitz from Nachrichten der Akademie der Wissenschaften in Göttingen, II. Mathematisch- Physikalische Klasse Jahrgang 1970, No. 7., 159–168.Google Scholar
  20. Holton, J. R., The Dynamic Meteorology of the Stratosphere and mesosphere (Amer. Meteor. Soc, 1975), 319 pp.Google Scholar
  21. Holton, J. R., and W. M. Wehrbein, (1980), A numerical model of the zonal mean circulation of the middle atmosphere, Pure and Appl. Geophys. 118, 284–306.CrossRefGoogle Scholar
  22. Leovy, C. B. (1964), Simple models of thermally driven mesospheric circulations, J. Atmos. Sci. 21, 327 341.Google Scholar
  23. Lindzen, R. S., and J. R. Holton (1968), A theory of the quasi-biennial oscillation, J. Atmos. Sci. 25, 1095–1107.CrossRefGoogle Scholar
  24. Longuet-Higgins, M. S. (1968), The eigenfunctions of Laplace’s tidal equations over a sphere, Phil. Trans. Roy. Soc. London 262, 511–607.CrossRefGoogle Scholar
  25. Mahlman, J. D., D. G. Andrews, D. L. Hartmann, T. Matsuno, and R. G. Murgatroyd, Transport of trace constituents in the stratosphere, in Dynamics of the Middle Atmosphere (J. R. Holton and T. Matsuno, eds.) (Terra Scientific 1984) pp. 387–416.Google Scholar
  26. Matsuno, T., and K. Nakamura (1979), The Eulerian and Lagrangian mean meridional circulations in the stratosphere at the time of a sudden warming, J. Atmos. Sci. 36, 640–654.CrossRefGoogle Scholar
  27. McIntyre, M. E. (1987), Dynamics and tracer transport in the middle atmosphere: An overview of some recent developments, Transport Processes in the Middle Atmosphere, (NATO Workshop Proceedings, Erice) G. Visconti, ed.Google Scholar
  28. Plumb, R. A. (1982), Zonally symmetric Hough modes and meridional circulations in the middle atmosphere, J. Atmos. Sci. 39, 983–991.Google Scholar
  29. Plumb, R. A., and R. C. Bell (1982) A model of the quasi-biennial oscillation on an equatorial beta-plane, Quant. J. Roy. Meteor. Soc. 108, 335–352.CrossRefGoogle Scholar
  30. Schneider, E. K. (1977), Axially symmetric steady-state models of the basic state for instability and climate studies. Part II: Nonlinear calculations, J. Atmos. Sci. 34, 280–297.CrossRefGoogle Scholar
  31. Tung, K. K. (1982), On the two-dimensional transport of stratospheric trace gases in isentropic coordinates, J. Atmos. Sci. 39, 2330–2355.CrossRefGoogle Scholar
  32. Tung, K. K. (1986), Nongeostrophic theory of zonally averaged circulation. Part I: Formulation, J. Atmos. Sci. 43, 2600.CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1989

Authors and Affiliations

  • Timothy J. Dunkerton
    • 1
  1. 1.Northwest Research Associates, Inc.BellevueUSA

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