• Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysics Series, Vol. 40, Academic Press, 489 pp.

  • Bannon, P. R., J. Schmidli, and C. Schär, 2003: On potential vorticity flux vectors. J. Atmos. Sci., 60, 29172921, doi:10.1175/1520-0469(2003)060<2917:OPVFV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bartels, J., D. Peters, and G. Schmitz, 1998: Climatological Ertel’s potential-vorticity flux and mean meridional circulation in the extra-tropical troposphere–lower stratosphere. Ann. Geophys., 16, 250265, doi:10.1007/s00585-998-0250-3.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C., and C. Schär, 1993: Flux of potential vorticity substance: A simple derivation and a uniqueness property. J. Atmos. Sci., 50, 18341836, doi:10.1175/1520-0469(1993)050<1834:FOPVSA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Danielsen, E., 1990: In defense of Ertel’s potential vorticity and its general applicability as a meteorological tracer. J. Atmos. Sci., 47, 20132020, doi:10.1175/1520-0469(1990)047<2013:IDOEPV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 2003: Comments on “A generalization of Bernoulli’s theorem.” J. Atmos. Sci., 60, 20392041, doi:10.1175/1520-0469(2003)060<2039:COAGOB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553587, doi:10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • Edmon, H. Jr., B. J. Hoskins, and M. McIntyre, 1980: Eliassen–Palm cross sections for the troposphere. J. Atmos. Sci., 37, 26002616, doi:10.1175/1520-0469(1980)037<2600:EPCSFT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ertel, H., 1942: Ein neuer hydrodynamischer Wirbelsatz (A new hydrodynamic eddy theorem). Meteor. Z., 59, 277281.

  • Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of isentropic distributions of potential vorticity in the presence of diabatic heating and fictional or other forces. J. Atmos. Sci., 44, 828841, doi:10.1175/1520-0469(1987)044<0828:OTEOVA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., and M. E. McIntyre, 1990: On the conservation and impermeability theorems for potential vorticity. J. Atmos. Sci., 47, 20212031, doi:10.1175/1520-0469(1990)047<2021:OTCAIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., J. Scinocca, and M. Greenslade, 2001: Formation and maintenance of the extratropical tropopause by baroclinic eddies. Geophys. Res. Lett., 28, 41794182, doi:10.1029/2001GL013485.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 1982: On the height of the tropopause and the static stability of the atmosphere. J. Atmos. Sci., 39, 412417, doi:10.1175/1520-0469(1982)039<0412:OTHOTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., and T. Schneider, 1999: The surface branch of the zonally averaged mass transport in the troposphere. J. Atmos. Sci., 56, 16881697, doi:10.1175/1520-0469(1999)056<1688:TSBOTZ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoinka, K.-P., 1998: Statistics of the global tropopause. Mon. Wea. Rev., 126, 33033325, doi:10.1175/1520-0493(1998)126<3303:SOTGTP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., 1991: Towards a PV-θ view of the general circulation. Tellus, 43A, 2735, doi:10.1034/j.1600-0870.1991.t01-3-00005.x.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877946, doi:10.1002/qj.49711147002.

    • Search Google Scholar
    • Export Citation
  • Johnson, D. R., 1989: The forcing and maintenance of global monsoonal circulations: An isentropic analysis. Adv. Geophys., 31, 43316, doi:10.1016/S0065-2687(08)60053-9.

    • Search Google Scholar
    • Export Citation
  • Kieu, C., and D.-L. Zhang, 2012: Is the isentropic surface always impermeable to the potential vorticity substance? Adv. Atmos. Sci., 29, 2935, doi:10.1007/s00376-011-0227-0.

    • Search Google Scholar
    • Export Citation
  • Koh, T.-Y., and R. Plumb, 2004: Isentropic zonal average formalism and the near-surface circulation. Quart. J. Roy. Meteor. Soc., 130, 16311653, doi:10.1256/qj.02.219.

    • Search Google Scholar
    • Export Citation
  • Mak, M., 2011: Atmospheric Dynamics. Cambridge University Press, 486 pp.

  • McIntyre, M. E., 2014: Potential vorticity. Encyclopedia of Atmospheric Science, G. R. North, J. Pyle, and F. Zhang, Eds., Elsevier, 375–383.

  • Oort, A., and J. Peixoto, 1983: Global angular momentum and energy balance measurements from observations. Adv. Geophys., 25, 355490, doi:10.1016/S0065-2687(08)60177-6.

    • Search Google Scholar
    • Export Citation
  • Schär, C., 1993: A generalization of Bernoulli’s theorem. J. Atmos. Sci., 50, 14371443, doi:10.1175/1520-0469(1993)050<1437:AGOBT>2.0.CO;2.

    • 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, doi:10.1175/JAS3341.1.

    • Search Google Scholar
    • Export Citation
  • Schneider, T., I. M. Held, and S. T. Garner, 2003: Boundary effects in potential vorticity dynamics. J. Atmos. Sci., 60, 10241040, doi:10.1175/1520-0469(2003)60<1024:BEIPVD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., S. A. Hausman, M. Garcia, K. V. Ooyama, and H.-C. Kuo, 2001: Potential vorticity in a moist atmosphere. J. Atmos. Sci., 58, 31483157, doi:10.1175/1520-0469(2001)058<3148:PVIAMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Truesdell, C., and R. Toupin, 1960: The classical field theories. Principles of Classical Mechanics and Field Theory, S. Flugge, Ed., Vol. III/1, Encyclopedia of Physics, Springer, 226–793 pp.

  • Vallis, G., 2006: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, 745 pp.

  • Viúdez, A., 1999: On Ertel’s potential vorticity theorem. On the impermeability theorem for potential vorticity. J. Atmos. Sci., 56, 507516, doi:10.1175/1520-0469(1999)056<0507:OESPVT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Viúdez, A., 2001: The relation between Beltrami’s material vorticity and Rossby–Ertel’s potential vorticity. J. Atmos. Sci., 58, 25092517, doi:10.1175/1520-0469(2001)058<2509:TRBBMV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yang, H., K. Tung, and E. Olaguer, 1990: Nongeostrophic theory of zonally averaged circulation. Part II: Eliassen–Palm flux divergence and isentropic mixing coefficient. J. Atmos. Sci., 47, 215241, doi:10.1175/1520-0469(1990)047<0215:NTOZAC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zdunkowski, W., and A. Bott, 2003: Dynamics of the Atmosphere: A Course in Theoretical Meteorology. Cambridge University Press, 738 pp.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 139 59 3
PDF Downloads 107 36 1

Aspects of Potential Vorticity Fluxes: Climatology and Impermeability

View More View Less
  • 1 Meteorological Institute, University of Munich, Munich, Germany
  • | 2 Institute for Atmospheric Physics, Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen, Germany
  • | 3 Geophysical Institute, University of Bergen, Bergen, Norway
Restricted access

Abstract

Some aspects of the dynamics of generalized potential vorticity (PV) density P = ω ⋅ χ are discussed with the main emphasis on P fluxes, where ωa is absolute vorticity and χ is a scalar. The impermeability theorem claims that there is no net P flux across a χ surface. Various forms of the flux are presented that mostly cross χ surfaces. As these fluxes are as dynamically relevant as the one chosen for the theorem, P fluxes through a surface element are inherently multivalued and there is no best choice on physical grounds. Nevertheless, the net P flux is unique for closed surfaces. This point is illustrated by P integrals over the volume between the earth’s surface and an isentropic surface. Reanalysis data are used to present mean advective and some nonadvective P fluxes for χ = θ in height coordinates. The extratropical tropopause appears to be supported by advective P fluxes. A satisfactorily closed P budget cannot, however, be presented.

Corresponding author address: Dr. Joseph Egger, Meteorological Institute, University of Munich, Theresienstr. 37, 80333 Munich, Germany. E-mail: j.egger@lrz.uni-muenchen.de

Abstract

Some aspects of the dynamics of generalized potential vorticity (PV) density P = ω ⋅ χ are discussed with the main emphasis on P fluxes, where ωa is absolute vorticity and χ is a scalar. The impermeability theorem claims that there is no net P flux across a χ surface. Various forms of the flux are presented that mostly cross χ surfaces. As these fluxes are as dynamically relevant as the one chosen for the theorem, P fluxes through a surface element are inherently multivalued and there is no best choice on physical grounds. Nevertheless, the net P flux is unique for closed surfaces. This point is illustrated by P integrals over the volume between the earth’s surface and an isentropic surface. Reanalysis data are used to present mean advective and some nonadvective P fluxes for χ = θ in height coordinates. The extratropical tropopause appears to be supported by advective P fluxes. A satisfactorily closed P budget cannot, however, be presented.

Corresponding author address: Dr. Joseph Egger, Meteorological Institute, University of Munich, Theresienstr. 37, 80333 Munich, Germany. E-mail: j.egger@lrz.uni-muenchen.de
Save