A Study of Eddy-induced Fluctuations of the Zonal-Mean Wind Using Conventional and Transformed Eulerian Diagnostics

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Abstract
The dynamics of eddy-induced fluctuations of the zonal-mean current in the troposphere and lower stratosphere is examined from the perspective of conventional and transformed Eulerian diagnostics using ECMWF FGGE IIIb data. Spatial correlations among different terms in the transformed Eulerian angular momentum equation for the entire FGGE year reveal a significant positive relationship between the divergence of the horizontal component of the Eliassen-Palm (E-P) flux (which is associated with meridional eddy fluxes of momentum) and day-to-day changes in the shape and intensity of the zonal current. It is found also that a very high negative correlation exists between the Coriolis torque associated with the eddy-induced residual circulation and the divergence of the vertical component of the E-P flux (which is associated with poleward eddy fluxes of heat and baroclinic wave development). An explanation is given as to why the Coriolis term in the transformed Eulerian momentum equation so effectively cancels the vertical E-P flux divergence and why the zonal current responds with such great sensitivity to the horizontal divergence. It is shown on theoretical grounds that in regions in which the stratification parameter S (which is proportional to the ratio of the square of the Brunt-Väisälä frequency to the square of the Coriolis frequency) is sufficiently small, the response of the zonal mean flow to the E-P flux divergence must be in the form of a residual circulation, with little change in the zonal angular momentum distribution. This is found to be the situation in regions of baroclinic wave development and intense poleward eddy heat fluxes. In regions of sufficiently large S the response to the E-P flux divergence must be in the form of an acceleration or deceleration of the zonal flow in the direction of the eddy torque, with very little effect on the residual circulation. This is found to be the situation in regions of horizontal wave propagation outside the source region where poleward eddy momentum fluxes dominate. A case study is selected from the FGGE dataset to illustrate the processes involved in a characteristic fluctuation of the zonal-mean current using both conventional and transformed Eulerian diagnostics. In this context the often neglected role of the poleward eddy heat flux at the lower boundary in accelerating the zonal current throughout the depth of the troposphere and lower stratosphere is shown to be important.

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