The Shape, Propagation and Mean-Flow Interaction of Large-Scale Weather Systems

For a zonal average operator the Eliassen-Palm flux provides a diagnostic of both eddy behavior and the feedback of the eddies onto the mean flow. This paper addresses the diagnosis problem for other averaging operators and, in particular, for time averaging which has proved in recent years such a powerful means of viewing the three-dimensional tropospheric flow. The horizontal velocity correlation tensor gives a measure of the characteristic horizontal eddy shape at a point. It also implies the direction of the group velocity relative to the mean flow in cases where such a concept is valid. However the major emphasis here is on the mean-flow feedback of eddies. In this respect, the eddy vorticity flux is determined by derivatives of the components of the anisotropic part of the tensor. Making a reasonable approximation allows the eddy vorticity flux convergence to be written in terms of E = (v′2 − u′2¯, u′v′¯). A simple interpretation of the mean flow feedback of eddies is then possible. A slightly more restrictive approximation allows the eddy shape and the sense of the relative group velocity to be determined also from E. The whole analysis may also be performed in the three-dimensional quasi-geostrophic case where it provides an approximate extension of the Eliassen-Palm flux concept. The theory and approximations are investigated for high-pass and low-pass transient eddies using data for single Northern and Southern Hemisphere winter seasons. The different signatures of the transient eddies in the two frequency bands are apparent and schematic pictures of the contrasting, dominant behavior in each band emerge. Data from one particular blocking event, when diagnosed using the theory developed here, give an indication of a positive feedback of the synoptic eddies onto the mean blocking flow.