Dynamics and Electrodynamics of the Mesosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 345

wave sources include surface wind flowover orographic features, frontal systems,
and severe storms; even earthquakes, nuclear explosions, and tsunamis have
created substantial waves in the atmosphere (see references inChapter 6). In brief,
if energy is to be conserved as an internal wave propagates upward, every time the
back gr ound density decreases by a factor of 2, the wave velocity must increase

by √ 2 or about 40%. In previous chapters we were most interested in those
waves that survived breaking and/or viscosity to create observable ionospheric
structure. We now investigate the wave breaking process, which can deposit
energy and momentum in the mesosphere.

7.2 Gravity Wave Breaking

Eventually most gravity waves will reach a height where their amplitude is so
great that they break like water waves on a beach. A good rule of thumb is that
a wave will break when its internal wave-induced velocity perturbation exceeds
its phase propagation speed. Then the wave particles overtake the wave phase
velocity and it steepens and breaks, as shown in Fig. 7.3 for a surface water wave
approaching a beach. An example of the breaking of an internal wave is shown
in Fig. 7.4. Here the velocity of a wave detected with the MU radar is plotted
along with the predicted change of amplitude with height without breaking. At
around 80 km the wave amplitude abruptly decays to values well below the linear
prediction ( e z / 2 H

curve. Wave breaking clearly has occurred.
For a gravity wave, the breaking criterion that the perturbation velocity
exceeds the wave phase velocity in the frame of the mean wind can be writ-
ten as (Orlanski and Bryan, 1969),

)

δ u /( c − u )> 1 (7.1)

where u is the p e rturbation amplitude, c is the horizontal wave phase velocity

component, and u is the component of the mean wind parallel to the wave vector.
From gravity wave theory, in which it is assumed that the flow is incompressible

δ

h

/k 5 gh

Figure 7.3 Simulation of water waves breaking on a beach.