A Multiscale Asymptotic Theory of Extratropical Wave–Mean Flow Interaction

Abstract

Abstract Multiscale asymptotic methods are used to derive wave activity equations for planetary- and synoptic-scale eddies and their interactions with a zonal mean flow. The eddies are assumed to be of small amplitude, and the synoptic-scale zonal and meridional length scales are taken to be equal. Under these assumptions, the zonal-mean and planetary-scale dynamics are planetary geostrophic (i.e., dominated by vortex stretching), and the interaction between planetary- and synoptic-scale eddies occurs only through the zonal mean flow or through diabatic processes. Planetary-scale heat fluxes are shown to enter the angular momentum budget through meridional mass redistribution. After averaging over synoptic length and time scales, momentum fluxes disappear from the synoptic-scale wave activity equation while synoptic-scale heat fluxes disappear from the baroclinicity equation, leaving planetary-scale heat fluxes as the only adiabatic term coupling the baroclinic and barotropic components of the zonal mean flow. In the special case of weak planetary waves, the decoupling between the baroclinic and barotropic parts of the flow is complete with momentum fluxes driving the barotropic zonal mean flow, heat fluxes driving the wave activity, and diabatic processes driving baroclinicity. These results help explain the apparent decoupling between the baroclinic and barotropic components of flow variability recently identified in observations and may provide a means of better understanding the link between thermodynamic and dynamic aspects of climate variability and change.