Self-Organization of Atmospheric Macroturbulence into Critical States of Weak Nonlinear Eddy–Eddy Interactions

Tapio Schneider California Institute of Technology, Pasadena, California

Search for other papers by Tapio Schneider in
Current site
Google Scholar
PubMed
Close
and
Christopher C. Walker California Institute of Technology, Pasadena, California

Search for other papers by Christopher C. Walker in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

It is generally held that atmospheric macroturbulence can be strongly nonlinear. Yet weakly nonlinear models successfully account for scales and structures of baroclinic eddies in Earth's atmosphere. Here a theory and simulations with an idealized GCM are presented that suggest weakly nonlinear models are so successful because atmospheric macroturbulence organizes itself into critical states of weak nonlinear eddy–eddy interactions. By modifying the thermal structure of the extratropical atmosphere such that its supercriticality remains limited, macroturbulence inhibits nonlinear eddy–eddy interactions and the concomitant inverse energy cascade from the length scales of baroclinic instability to larger scales. For small meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are set by radiation and convection, and the supercriticality is less than one; for sufficiently large meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are modified by baroclinic eddies such that the supercriticality does not significantly exceed one. In either case, the scale of the energy-containing eddies is similar to the scale of the linearly most unstable baroclinic waves, and eddy kinetic and available potential energies are equipartitioned. The theory and simulations point to fundamental constraints on the thermal structures and global circulations of the atmospheres of Earth and other planets, for example, by providing limits on the tropopause height and estimates for eddy scales, eddy energies, and jet separation scales.

Corresponding author address: Tapio Schneider, California Institute of Technology, Mail Code 100-23, 1200 E. California Blvd., Pasadena, CA 91125. Email: tapio@caltech.edu

Abstract

It is generally held that atmospheric macroturbulence can be strongly nonlinear. Yet weakly nonlinear models successfully account for scales and structures of baroclinic eddies in Earth's atmosphere. Here a theory and simulations with an idealized GCM are presented that suggest weakly nonlinear models are so successful because atmospheric macroturbulence organizes itself into critical states of weak nonlinear eddy–eddy interactions. By modifying the thermal structure of the extratropical atmosphere such that its supercriticality remains limited, macroturbulence inhibits nonlinear eddy–eddy interactions and the concomitant inverse energy cascade from the length scales of baroclinic instability to larger scales. For small meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are set by radiation and convection, and the supercriticality is less than one; for sufficiently large meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are modified by baroclinic eddies such that the supercriticality does not significantly exceed one. In either case, the scale of the energy-containing eddies is similar to the scale of the linearly most unstable baroclinic waves, and eddy kinetic and available potential energies are equipartitioned. The theory and simulations point to fundamental constraints on the thermal structures and global circulations of the atmospheres of Earth and other planets, for example, by providing limits on the tropopause height and estimates for eddy scales, eddy energies, and jet separation scales.

Corresponding author address: Tapio Schneider, California Institute of Technology, Mail Code 100-23, 1200 E. California Blvd., Pasadena, CA 91125. Email: tapio@caltech.edu

Save
  • Betts, A. K., 1986: A new convective adjustment scheme. Part I: Observational and theoretical basis. Quart. J. Roy. Meteor. Soc, 112 , 677691.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc, 112 , 693709.

    • Search Google Scholar
    • Export Citation
  • Boer, G. J., 1983: Homogeneous and isotropic turbulence on the sphere. J. Atmos. Sci, 40 , 154163.

  • Boer, G. J., and T. G. Shepherd, 1983: Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci, 40 , 164184.

  • Bourke, W., 1974: A multilevel spectral model. I. Formulation and hemispheric integrations. Mon. Wea. Rev, 102 , 687701.

  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci, 28 , 10871095.

  • Cho, J. Y-K., and L. M. Polvani, 1996: The morphogenesis of bands and zonal winds in the atmospheres on the giant outer planets. Science, 273 , 335337.

    • Search Google Scholar
    • Export Citation
  • Frederiksen, J. S., 1983: Disturbances and eddy fluxes in Northern Hemisphere flows: Instability of three-dimensional January and July flows. J. Atmos. Sci, 40 , 836855.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 1978: The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parameterizations. J. Atmos. Sci, 35 , 572576.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 1982: On the height of the tropopause and the static stability of the troposphere. J. Atmos. Sci, 39 , 412417.

  • Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc, 75 , 18251830.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., and V. D. Larichev, 1996: A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta-plane. J. Atmos. Sci, 53 , 946952.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., and T. Schneider, 1999: The surface branch of the zonally averaged mass transport circulation in the troposphere. J. Atmos. Sci, 56 , 16881697.

    • Search Google Scholar
    • Export Citation
  • Holloway, G., 1986: Estimation of oceanic eddy transports from satellite altimetry. Nature, 323 , 243244.

  • Ingersoll, A. P., and H. Kanamori, 1995: Waves from the collisions of comet Shoemaker-Levy 9 with Jupiter. Nature, 374 , 706708.

  • Ingersoll, A. P., P. J. Gierasch, D. Banfield, and A. R. Vasavada, and the Galileo Imaging Team, 2000: Moist convection as an energy source for the large-scale motions in Jupiter's atmosphere. Nature, 403 , 630632.

    • Search Google Scholar
    • Export Citation
  • Ingersoll, A. P., and Coauthors, 2004: Dynamics of Jupiter's atmosphere. Jupiter: The Planet, Satellites, and Magnetosphere, F. Bagenal, T. E. Dowling, and W. B. McKinnon, Eds., Cambridge University Press, 748 pp.

    • Search Google Scholar
    • Export Citation
  • Kållberg, P., A. Simmons, S. Uppala, and M. Fuentes, 2004: The ERA-40 archive. Tech. Rep., European Centre for Medium- Range Weather Forecasts, Reading, United Kingdom, 31 pp. [Available online at www.ecmwf.int/publications.].

  • Kushner, P. J., and I. M. Held, 1998: A test, using atmospheric data, of a method for estimating oceanic eddy diffusivity. Geophys. Res. Lett, 25 , 42134216.

    • Search Google Scholar
    • Export Citation
  • Lapeyre, G., and I. M. Held, 2003: Diffusivity, kinetic energy dissipation, and closure theories for the poleward eddy heat flux. J. Atmos. Sci, 60 , 29072916.

    • Search Google Scholar
    • Export Citation
  • Lau, N-G., 1978: On the three-dimensional structure of the observed transient eddy statistics of the Northern Hemisphere wintertime circulation. J. Atmos. Sci, 35 , 19001923.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1993: Baroclinic neutrality and the tropopause. J. Atmos. Sci, 50 , 11481151.

  • Lindzen, R. S., and B. Farrell, 1980a: The role of the polar regions in global climate, and a new parameterization of global heat transport. Mon. Wea. Rev, 108 , 20642079.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., and B. Farrell, 1980b: A simple approximate result for the maximum growth rate of baroclinic instabilities. J. Atmos. Sci, 37 , 16481654.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7 , 157167.

  • Morse, P. M., and H. Feshbach, 1953: Methods of Theoretical Physics. International Series in Pure and Applied Physics, McGraw-Hill, 1978 pp.

    • Search Google Scholar
    • Export Citation
  • Panetta, R. L., 1993: Zonal jets in wide baroclinically unstable regions: Persistence and scale separation. J. Atmos. Sci, 50 , 20732106.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1970: Finite-amplitude baroclinic waves. J. Atmos. Sci, 27 , 1530.

  • Pedlosky, J., 1979: Finite-amplitude baroclinic waves in a continuous model of the atmosphere. J. Atmos. Sci, 36 , 19081924.

  • Rhines, P. B., 1975: Waves and turbulence on a β-plane. J. Fluid Mech, 69 , 417443.

  • Salmon, R., 1980: Baroclinic instability and geostrophic turbulence. Geophys. Astrophys. Fluid Dyn, 15 , 167211.

  • Santer, B. D., and Coauthors, 2003: Contributions of anthropogenic and natural forcing to recent tropopause height changes. Science, 301 , 479483.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., 2004: The tropopause and the thermal stratification in the extratropics of a dry atmosphere. J. Atmos. Sci, 61 , 13171340.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., 2005: Zonal momentum balance, potential vorticity dynamics, and mass fluxes on near-surface isentropes. J. Atmos. Sci, 62 , 18841900.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., 2006: The thermal stratification of the extratropical troposphere. The Global Circulation of the Atmosphere: Phenomena, Theory, Challenges, T. Schneider and A. H. Sobel, Eds., Princeton University Press, in press. [Available online at www.gps.caltech.edu/~tapio.].

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 1987: A spectral view of nonlinear fluxes and stationary–transient interaction in the atmosphere. J. Atmos. Sci, 44 , 11661178.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., and B. J. Hoskins, 1976: Baroclinic instability on the sphere: Normal modes of the primitive and quasigeostrophic equations. J. Atmos. Sci, 33 , 14541477.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., and B. J. Hoskins, 1977: Baroclinic instability on the sphere: Solutions with a more realistic tropopause. J. Atmos. Sci, 34 , 581588.

    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., S. Manabe, and J. L. Holloway Jr., 1965: Numerical results from a nine-level general circulation model of the atmosphere. Mon. Wea. Rev, 93 , 727768.

    • Search Google Scholar
    • Export Citation
  • Smith, K. S., and G. K. Vallis, 2002: The scales and equilibration of midocean eddies: Forced-dissipative flow. J. Phys. Oceanogr, 32 , 16991720.

    • Search Google Scholar
    • Export Citation
  • Stone, P. H., 1978: Baroclinic adjustment. J. Atmos. Sci, 35 , 561571.

  • Stone, P. H., and B. Nemet, 1996: Baroclinic adjustment: A comparison between theory, observations, and models. J. Atmos. Sci, 53 , 16631674.

    • Search Google Scholar
    • Export Citation
  • Straus, D. M., and P. Ditlevsen, 1999: Two-dimensional turbulence properties of the ECMWF reanalyses. Tellus, 51A , 749772.

  • Thuburn, J., and G. C. Craig, 1997: GCM tests of theories for the height of the tropopause. J. Atmos. Sci, 54 , 869882.

  • Valdes, P. J., and B. J. Hoskins, 1988: Baroclinic instability of the zonally averaged flow with boundary layer damping. J. Atmos. Sci, 45 , 15841593.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., and M. E. Maltrud, 1993: Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr, 23 , 13461362.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 738 288 23
PDF Downloads 587 217 14