Dynamics and Electrodynamics of the Mesosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 348

h

Wave velocity

h 0

u max

Wind speed

Figure 7.5 Conditions for wave absorption by the jet stream.

cooling, a wave-driven refrigeration process. The opposite effect occurs at the
winter pole and the temperature rises.
This preferential direction of momentum transfer could arise in a variety of
ways and we only discuss one here, the so-called critical layer effect. Gravity
waves are created by weather processes and it is no surprise that their phase
velocities are small enough that jet stream winds are often larger than the wave
propagation speeds. Suppose, then, that a wave propagates upward to a height
where its velocity equals that of the background wind at, say, height h 0 in
Fig. 7.5. In general, the Doppler-shifted frequency in the wind frame ( ω )is

given by

ω = ω − k · u (7.6)

ω

where 0

and the wave is Doppler-shifted to zero. In this case the wave is not a wave at
all, just some eddy in the flow, and it ceases to exist. In fact, only waves with
horizontal velocities greater than u max get through the jet stream at all. Waves
propagating in the other direction, against the flow, are Doppler-shifted upward
and pass through easily. Eventually these waves will break at altitudes above
the jet and deposit their momentum. Since the jet stream is to the west in the
summer and to the east in the winter, gravity wave filtering thus can lead to the
refrigeration mechanism just described above and to the observed temperature
asymmetry.
Modern global circulation models can only include such effects by param-
eterizing momentum fluxes. One such model (Roble and Ridley, 1994) is the
TIME-GCM (Thermosphere-Ionosphere-Mesosphere-Electrodynamics General
Circulation Model). Their calculated yearly variation of temperature at 85 km is

ω , k , and u are measured in the earth frame. At h = h 0 , then, =