Aspects of Potential Vorticity Fluxes: Climatology and Impermeability

Joseph Egger Meteorological Institute, University of Munich, Munich, Germany

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Klaus-Peter Hoinka Institute for Atmospheric Physics, Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen, Germany

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Thomas Spengler Geophysical Institute, University of Bergen, Bergen, Norway

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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
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