Aspects of potential vorticity fluxes, climatology and impermeability

Abstract

Some aspects of the dynamics of generalized potential vorticity (PV) density P = Omega x grad chi x are discussed with the main emphasis on P fluxes, where va is absolute vorticity and chi is a scalar. The impermeability theorem claims that there is no net P flux across a chi surface. Various forms of the flux are presented that mostly cross chi 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 byPintegrals 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 chi = theta in height coordinates. The extratropical tropopause appears to be supported by advective P fluxes. A satisfactorily closed P budget cannot, however, be presented.