Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M., andI. A. Stegun,Handbook of Mathematical Functions (National Bureau of Standards, Washington D.C. 1970) 1046 pp.
Andrews, D. G., andM. 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.
Boyd, J. P., andZ. D. Christidis (1982),Low wavenumber instability on the equatorial beta-plane, Geophys. Res. Lett.,9, 769–772.
Delisi, D. P., andT. J. Dunkerton (1988),Seasonal variation of the semiannual oscillaton, J. Atmos. Sci., to appear.
Dickinson, R. E. (1968),On the excitation and propagation of zonal winds in an atmosphere with Newtonian cooling, J. Atmos. Sci.25, 269–279.
Dunkerton, T. J. (1978),On the mean meridional mass motions of the stratosphere and mesosphere, J. Atmos. Sci.35, 2325–2333.
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.
Dunkerton, T. J. (1981),On the inertial stability of the equatorial middle atmosphere, J. Atmos. Sci.38, 2354–2364.
Dunkerton, T. J. (1983),A nonsymmetric equatorial inertial instability, J. Atmos. Sci.40, 807–813.
Dunkerton, T. J. (1985),A two-dimensional model of the quasi-biennial oscillation, J. Atmos. Sci.42, 1151–1160.
Dunkerton, T. J. (1988),Body force circulation and the Antarctic ozone minimum, J. Atmos. Sci.45, 427–438.
Dunkerton, T. J. (1989),Nonlinear Hadley circulation driven by asymmetric differential heating. J. Atmos. Sci., to appear.
Dunkerton, T. J., C.-P. F. Hsu, andM. E. McIntyre (1981),Some Eulerian and Lagrangian diagnostics for a model stratospheric warming, J. Atmos. Sci.38, 819–843.
Edmon, H. J., B. J. Hoskins, andM. E. McIntyre (1980),Eliassen-Palm cross sections for the troposphere, J. Atmos. Sci.37, 2600–2616.
Eliassen, A. (1951),Slow thermally or frictionally controlled meridional criculation in a circular vortex, Astrophys. Norv.5, 19–60.
Flattery, T. W. (1967),Hough Functions, Technical Report No. 21, Dept. of Geophysical Sciences, University of Chicago, 175 pp.
Garcia, R. R. (1987),On the mean meridional circulation of the middle atmosphere, J. Atmos. Sci.44, 3599–3609.
Held, I. M., andA. Y. Hou (1980),Nonlinear axially symmetric circulations in a nearly inviscid atmosphere, J. Atmos. Sci.37, 515–533.
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.
Holton, J. R.,The Dynamic Meteorology of the Stratosphere and Mesosphere (Amer. Meteor. Soc., 1975), 319 pp.
Holton, J. R., andW. M. Wehrbein, (1980),A numerical model of the zonal mean circulation of the middle atmosphere, Pure and Appl. Geophys.118, 284–306.
Leovy, C. B. (1964),Simple models of thermally driven mesospheric circulations, J. Atmos. Sci.21, 327–341.
Lindzen, R. S., andJ. R. Holton (1968),A theory of the quasi-biennial oscillation, J. Atmos. Sci.25, 1095–1107.
Longuet-Higgins, M. S. (1968),The eigenfunctions of Laplace's tidal equations over a sphere, Phil. Trans. Roy. Soc. London262, 511–607.
Mahlman, J. D., D. G. Andrews, D. L. Hartmann, T. Matsuno, andR. G. Murgatroyd,Transport of trace constituents in the stratosphere, inDynamics of the Middle Atmosphere (J. R. Holton and T. Matsuno, eds.) (Terra Scientific 1984) pp. 387–416.
Matsuno, T., andK. 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.
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.
Plumb, R. A. (1982),Zonally symmetric Hough modes and meridional circulations in the middle atmosphere, J. Atmos. Sci.39, 983–991.
Plumb, R. A., andR. C. Bell (1982)A model of the quasi-biennial oscillation on an equatorial beta-plane, Quant. J. Roy. Meteor. Soc.108, 335–352.
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.
Tung, K. K. (1982),On the two-dimensional transport of stratospheric trace gases in isentropic coordinates, J. Atmos. Sci.39, 2330–2355.
Tung, K. K. (1986),Nongeostrophic theory of zonally averaged circulation. Part I: Formulation, J. Atmos. Sci.43, 2600.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dunkerton, T.J. Body force circulations in a compressible atmosphere: Key concepts. PAGEOPH 130, 243–262 (1989). https://doi.org/10.1007/BF00874458
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00874458