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provides an upward directed EP flux contribution. This dominates over the verti-
cal momentum flux, and the net result is that the Rossby-gravity mode transfers
easterly momentum upward and can provide a momentum source for the easterly
phase of the QBO. Observed Kelvin and Rossby-gravity wave momentum fluxes
are not, however, sufficient to account for the observed zonal accelerations of the
QBO. Additional wave sources, such as gravity waves generated by convective
storms, must also contribute to the forcing of the QBO.
It was pointed out in Section 12.4 that quasi-geostrophic wave modes do not pro-
duce any net mean flow acceleration unless the waves are transient or are damped
mechanically or thermally. Similar considerations apply to gravity waves and to
the equatorial Kelvin and Rossby-gravity modes. Stratospheric waves are subject
to thermal damping by infrared radiation, and to both thermal and mechanical
damping by small-scale turbulent motions. Such damping is strongly dependent
on the Doppler-shifted frequency of the waves. As the Doppler-shifted frequency
decreases, the vertical component of group velocity also decreases, and there
is a longer time available for the wave energy to be damped as it propagates
through a given vertical distance. Thus, eastward propagating gravity waves and
Kelvin waves tend to be damped preferentially in westerly shear zones, where
their Doppler-shifted frequencies decrease with height. The momentum flux con-
vergence associated with this damping provides a westerly acceleration of the
mean flow, and thus causes the westerly shear zone to descend. Similarly, the
westward propagating gravity waves and Rossby-gravity waves are damped in
easterly shear zones, thereby causing an easterly acceleration and descent of the
easterly shear zone. We conclude that the QBO is indeed excited primarily by
vertically propagating waves through wave transience and damping, which causes
westerly accelerations in westerly shear zones and easterly accelerations in easterly
shear zones.
This process of wave, mean-flow interaction can be elucidated by considering
the heavy wavy lines in Figs. 12.12 and 12.13. These lines indicate the verti-
cal displacement of horizontal surfaces of fluid parcels (material surfaces) by the
velocity field associated with the waves. (For sufficiently weak thermal damping
they are approximately the same as isentropic surfaces.) The wavy lines show that
the maximum upward displacement occurs 1/4 cycle after the maximum upward
perturbation velocity. In the Kelvin wave case (Fig. 12.12), positive pressure per-
turbations coincide with negative material surface slopes. Thus, the fluid below a
wavy material line exerts an eastward directed pressure force on the fluid above.
Because the wave amplitude decreases with height, this force is larger for the lower
of the two material lines in Fig. 12.12. There will thus be a net westerly acceler-
ation of the block of fluid contained between the two wavy material lines shown
in Fig. 12.12. For the Rossby-gravity wave, however, positive pressure perturba-
tions coincide with positive slopes of the material lines. There is thus a westward
directed force exerted by the fluid below the lines on the fluid above as shown in
Fig. 12.13. In this case the result is a net easterly acceleration of the fluid contained
