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The wave forcing

To further study the relations between the eddy flux and the vacillations we now present lagged cross covariances between the zonal mean zonal wind and the terms in the zonal momentum balance equation, i.e., the zonal mean wind tendency $\partial \overline{u}/ \partial t$, the Coriolis term $f \overline{v}^{*}$, and the two components of the eddy forcing
 We chose the zonal mean zonal wind at 10 hPa and concentrate as before on 60 N. The covariances with the tendency  (fFig 5, top) are easily understood: at 10 hPa large (small) values of the zonal wind have been preceded by acceleration (deceleration) and  are followed by deceleration (acceleration). The vertical tilt in cross-over between positive and negative covariances is an effect of the downward propagation.

The strong similarity between the first and last panel in Fig. 5 shows that the downward propagation is driven by wave mean interactions related to the waves resolved in the reanalysis. We also note that the vertical wave flux dominates and that the horizontal wave flux only plays a minor role in the stratosphere.

Figure 5 Covariance between the zonal mean wind at 10 hPa, 60 N and the terms in the balance equation for zonal momentum as function of lag  (days) and pressure. Shading as in Fig. 2.