Lau, N-C., and E. O. Holopainen, 1984: Transient eddy forcing of the time-mean flow as identified by geopotential tendencies. Journal of the Atmospheric Sciences, 41 (3), 313-328.

Abstract: The forcing of the time-mean flow by transient eddies is examined within the framework of a quasi-geostrophic equation relating the geopotential tendency to the convergence of transient eddy transports of heat and vorticity. The forcing functions of this equation are computed using observed circulation statistics for the wintertime Northern Hemisphere, and solutions are sought for the three-dimensional structure of geopotential and temperature tendencies associated with eddies of different time scales.
In general, the geopotential tendencies associated with vorticity fluxes are of the same sign within a given atmospheric column; whereas the polarity of the geopotential tendencies associated with heat fluxes in the lower troposphere is opposite to that in the upper troposphere. The geostrophic wind tendencies associated with synoptic-scale eddies with periods between 2.5 and 6 days are strongest in the vicinity of the oceanic storm tracks. The enhanced poleward heat transports by active disturbances in these regions lead to eastward accelerations of the geostrophic flow in the lower troposphere, westward accelerations in the upper troposphere, and hence a reduction in the vertical shear of the eastward flow along the storm tracks. The vorticity transports by eddies with synoptic time scales are associated with eastward accelerations throughout the troposphere over the storm tracks. The geostrophic wind tendencies associated with the vorticity fluxes tend to dominate in the upper troposphere, so that the combined effect of the eddy transports of heat and vorticity by synoptic-scale eddies is to accelerate the eastward current at all vertical levels in middle latitudes. The geopotential tendencies associated with eddies with periods between 10 days and a season are generally stronger than those associated with synoptic-scale disturbances. In the upper troposphere, the transports of both heat and vorticity by the low-frequency eddies are accompanied by tendencies which act to destroy the departure from zonal symmetry of the time-averaged geopotential height field. The forcing of the geopotential height field due to vorticity transports by low-frequency eddies is stronger than the corresponding forcing due to heat transports.
The temperature tendencies associated with eddy heat transports are much stronger than those associated with eddy vorticity transports. The thermal forcing due to synoptic-scale disturbances is characterized by dipole-like structures over the western oceans, with positive temperature tendencies (warming) north of the cyclonic tracks and negative tendencies (cooling) further south. In the lower troposphere, the tendencies associated with low-frequency eddies act to destroy the zonally asymmetric component of the stationary temperature field. The typical magnitude of temperature tendencies as computed using the present method, which implicitly takes into acount the combined effects of eddy flux convergences and the associated secondary circulations, is about 60-70% of the corresponding values obtained by considering the convergence of eddy heat fluxes alone.
The effects of transient disturbances as depicted by tendencies associated with eddy fluxes are contrasted with earlier results based on eddy transports of quasi-geostrophic potential vorticity. The distinction between these two approaches is discussed.