A New Three-Dimensional Residual Flow Theory and Its Application to Brewer–Dobson Circulation in the Middle and Upper Stratosphere

Abstract This study formulates three-dimensional (3D) residual flow, treating both stationary and transient waves. The zonal meridional momentum equations contain four terms: the geostrophic wind tendency, Coriolis force for horizontal product of potential vorticity other than constant planetary vorticity, friction. thermodynamic equation contains three temperature advection basic by vertical diabatic heating. mean 3D flow equals time transformed Eulerian-mean equations. new is sum that derived Plumb waves quadratic terms time-mean fields, which correspond approximately to Stokes correction due are symmetric in directions, contrast with those formulated Kinoshita et al., treat zonal-mean as wind. newly formulas applied climatology structure deep branch Brewer–Dobson circulation. In Northern Hemisphere December–February, flows directed inward toward polar vortex strongly over east Siberia, where downward maximized, weakly Atlantic; meanwhile, they outward from North America Europe. A longitudinal dependence poleward also observed Southern June–August.