Lau, N-C., and J. M. Wallace, 1979: On the distribution of horizontal transports by transient eddies in the northern hemisphere wintertime circulation. Journal of the Atmospheric Sciences, 36 (10), 1844-1861.

Abstract: Horizontal fluxes in geopotential, heat, zonal momentum, relative vorticity and potential vorticity by the transient eddies on selected pressure surfaces are computed on the basis of data from twice daily synoptic charts for the Northern Hemisphere, objectively analyzed at the National Meteorological Center. The distribution of fluxes is resolved into nondivergent and irrotational parts and displayed in a vectorial format.
The nondivergent flux of geopotential closely parallels contours of constant temporal variance of geopotential. Nondivergent transient eddy fluxes of heat, relative vorticity and potential vorticity, all evaluated in the vicinity of the tropopause level, bear a similar but less exact relation to the distribution of the temporal variance of geopotential. These relationships are shown to exist because 1) the wind field responsible for the fluxes is quasi-geostrophic and 2) the instantaneous distributions of temperature, relative vorticity and potential vorticity tend to be rather similar to that of the geopotential field in the vicinity of the tropopause level. For these three parameters and for geopotential, the nondivergent fluxes at the tropopause level tend to be considerably larger than the corresponding irrotational fluxes.
The distribution of transient eddy heat flux in the lower troposphere is primarily irrotational and directed down the local horizontal gradient of the time-averaged temperature field. The magnitudes of these fluxes are comparable to those of corresponding fluxes associated with horizontal temperature advection by the time-averaged flow. There does not appear to be any simple functional relationship between the scalar magnitudes of the fluxes and local mean temperature gradients. The irrotational transient eddy heat fluxes at 300 mb resemble the distribution of total transient eddy heat flux at 850 mb. At the 200 mb level these fluxes are primarily countergradient in middle latitudes.
The irrotational transient eddy flux of zonal momentum at the jet stream level is much smaller than the corresponding flux associated with momentum advection by the time-averaged flow and it is directed into regions of low zonal wind speed. The irrotational flux of geopotential is directed out of regions of decaying transient disturbances and into regions of cyclogenesis.
The irrotational fluxes of vorticity and potential vorticity near the jet stream level are very similar. Their distribution appears to be strongly related to the time-averaged sea level pressure field, with fluxes out of regions of high sea level pressure and into regions of low pressure. These transports appear to be in the proper sense to fulfill the balance requirements for vorticity and potential vorticity. The divergence of the transient eddy flux of potential vorticity is weaker than the horizontal advection of potential vorticity by the time-averaged flow. It is suggested that the observed distribution of potential vorticity flux is imposed on the transient eddies by the distribution of sources and sinks of potential vorticity at the earth's surface which are closely related to the sea level pressure distribution.