Comparison of conventional and transformed in the troposphere

The effect of synoptic‐scale transient eddies on the mean zonal current in the troposphere and lower stratosphere is examined using conventional and transformed Eulerian diagnostics. In each case the partial solution of the Eliassen‐Kuo diagnostic equation for the meridional circulation is obtained using as forcing functions only transient eddy (TE) fluxes of heat and momentum. This solution is then used to calculate the Coriolis force and the advective terms in the zonal mean momentum equation. the ‘transient‐eddy‐induced’ zonal momentum tendency is defined as the sum of these terms and the eddy flux terms in the zonal momentum equation. Although conventional and transformed Eulerian diagnostics give the same transient‐eddy‐induced momentum and kinetic energy tendencies, the interpretation of the mechanisms involved is different. It is found that the TE flux convergence of momentum, which is regarded as the torque in the conventional diagnostics, correlates better with the TE‐induced zonal momentum tendency in the troposphere and lower stratosphere than does the transient E‐P flux divergence, which is regarded as the effective torque in the transformed diagnostics. In the latter formalism, the Coriolis force acting on the residual meridional circulation is larger in magnitude than the E‐P flux divergence and is of opposite sign. the net zonal wind acceleration is given by an extremely small difference between these two large quantities and is largely opposite to the E‐P flux divergence. Moreover. the role of the TE heat flux in this formalism is found to be negligible, with the poleward heat flux at the boundary and in the interior inducing accelerations of almost equal magnitude and opposite sign. Some insight into the role of the transient E‐P flux divergence and its components is sought by examining a form of potential vorticity equation for the zonally averaged current, in which the residual meridional circulation has been eliminated. This relationship reveals the importance of the horizontal derivatives of the E‐P flux divergence in forcing zonal wind accelerations, and elucidates most vividly the role of the rotational stratification parameter in diminishing the impact of wave action at high latitudes in the middle troposphere. Examination of the numerical influence function corresponding to the differential operator which operates on the zonal momentum tendency in this equation reveals why the TE flux of heat, which peaks at a higher latitude and lower altitude than the TE flux convergence of momentum, is much less effective in accelerating the zonal current.