Dynamics and Electrodynamics of the Mesosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 347

But if N 2 is negative the parcel does not return to its equilibrium position and
the atmosphere is said to be convectively unstable. Taking the spatial derivative
of (7.2) and ignoring the second derivative of the background potential temper-
ature profile gives

N 0 1

δ u

N 2 ( z ) = − (7.5)

−

c u

where N 0 is the mean background Brunt-Väisälä frequency. Thus, condition
is identica l to the convective instability condition (7.1) for the region since for
δ , N 2

u is negative.

Panel b in Fig. 7.4 shows the wave-induced N 2

>( c − u ) ( z )

for the event using (7.5)
for both the actual data set and the extrapolated wave field using the e z / 2 H fac-
tor. Clearly, N 2 was going to become negative at 80 km, the height where the
wave broke. The fact that the measured N 2 did not actually become negative
may be due to the fact that observations almost always occur in the fully non-
linear regime. But another possibility is shown in panel c. Here the extrapolated
Richardson number is plotted. It becomes less than 0.25 at 79 km, suggesting that
a shear instability may have set in at a lower height than the convective instabil-
ity. In any case, the wave clearly broke. The fact that its amplitude dipped to less
than one-half of its value where breaking should occur is surprising. Theorists
have speculated that the wave amplitude would stay at the amplitude where
breaking occurs. But recent simulations (D. Fritts, personal communication,
2001) indicate that wave amplitudes drop well below this value due to rapid
energy dissipation and then start to grow again with altitude before breaking
again.

( z )

7.3 The Polar Summer Mesosphere: A Wave-Driven
Refrigerator

But what does this have to with the cold summer mesopause? When waves break
on a beach or in the clear air they deposit their energy and momentum back into
the local medium (swimmers in a rip current know this very well). The meso-
sphere is so tenuous that the input of momentum from waves generated in the
dense lower atmosphere is very significant. Current theories of the mesosphere
argue that the waves that reach these heights come from preferred directions
that are different in the two hemispheres. In the summer hemisphere the waves
preferentially come from the west depositing a net eastward momentum into the
medium. This spins the atmosphere up somewhat and it moves away from the
pole. To conserve mass there is a net upflow at high latitudes resulting in adiabatic