Three-Dimensional Propagation of Transient Quasi-Geostrophic Eddies and Its Relationship with the Eddy Forcing of the Time—Mean Flow

Abstract

An approximate theory is developed of small-amplitude transient eddies on a slowly varying time-mean flow. Central to this theory is a flux M_T, which in most respects constitutes a generalization of the Eliassen–Palm flux to three dimensions; it is a conservable measure of the flux of eddy activity (for small amplitude transients) and is parallel to group velocity for an almost-plane wave train. The use of this flux as a diagnostic of transient eddy propagation is demonstrated by application of the theory to a ten-year climatology of the Northern Hemisphere winter circulation. Results show the anticipated concentration of eddy flux along the major storm tracks. While, in a suitably transformed system, M_T may be regarded as a flux of upstream momentum, it is not a complete description of the eddy forcing of the mean flow; additional effects arise due to downstream transience (i.e., spatial inhomogeneity in the direction of the time-mean flow) of the eddy amplitudes. The relation between M_T and the “E-vector” of Hoskins et al. is discussed.