Zonal momentum balance, potential vorticity dynamics, and mass fluxes on near-surface isentropes
While it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in potential vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean balance of zonal momentum and of potential vorticity on isentropes, including the near-surface isentropes that sometimes intersect the surface. Integrated vertically, the mean zonal momentum or potential vorticity balance leads to a balance condition that relates the mean meridional mass flux along isentropes to eddy fluxes of potential vorticity and surface potential temperature. The isentropic-coordinate balance condition formally resembles balance conditions well known in quasigeostrophic theory, but on near-surface isentropes it generally differs from the quasigeostrophic balance conditions. Not taking the intersection of isentropes with the surface into account, quasigeostrophic theory does not adequately represent the potential vorticity dynamics and mass fluxes on near-surface isentropes—a shortcoming that calls into question the relevance of quasigeostrophic theories for the macroturbulence and global circulation of the atmosphere.
© 2005 American Meteorological Society. Manuscript received 2 December 2003, in final form 13 October 2004. I am grateful to Chris Walker for performing the simulations with the idealized GCM and for providing analyses of observational data with which I verified the scaling estimates of section 3e; to Isaac Held for discussions that helped to clarify commonalities and differences between dynamics in isentropic coordinates and in quasigeostrophic theory; to Tieh-Yong Koh and Peter Haynes for comments on drafts of this paper; and to the Davidow Research Fund for financial support. The balance condition (12) was originally included in a section of a paper jointly authored with Isaac Held and Stephen Garner (Schneider et al. 2003), a section that was later removed to reduce the length of that paper. I thank Isaac Held and Stephen Garner for helpful discussions during the writing of that section.