Geoscience Reference
In-Depth Information
Condor velocities with AMISR vertical, AMISR 20°
JULIA vertical, JULIA 23
and JULIA 51
west beams
150
100
50
0
0
50
100
150
Ground range (km)
Figure 4.35b
Regions in which these radars would record a Doppler shift
9
C
s
in
the presence of a zero-order horizontal drift, as in Fig. 3.17b, and vertical perturbation
drifts, as in Fig. 4.35a, are indicated in red. [After Kelley et al. (2008). Reproduced with
permission of the American Geophysical Union.] See Color Plate 7.
≥
.
0
.
4.8.3 Nonlinear Gradient Drift Theories
Extensive analytical and simulation studies have been performed on the
intermediate-scale (
≤
100m) type 2 or gradient drift irregularities. These studies
permit a detailed comparison between theoretical results and the radar and rocket
data. McDonald et al. (1974, 1975) studied numerically the nonlinear evolution
of small-scale (
λ
10m) type 2 irregularities by using a grid of 50
×
50 points
with a mesh spacing of 1
5m in both horizontal and vertical directions. They
observed that intermediate wavelengths (
.
28m) are excited only after the
large-scale primary horizontally propagating waves grow to an amplitude of 4%,
consistent with the “two-step” theory outlined previously. The quasi-final state
is highly turbulent and almost two-dimensionally isotropic, in agreement with
the radar observations. Figure 4.36 shows the saturated nonlinear development
of the gradient drift irregularities found in these simulations. In the turbulent
state the small-scale irregularities have upward and downward motions with
speeds comparable to the background horizontal drift. The two-dimensional
power spectra of
λ<
2
were found to be proportional to
k
−
3
.
5
. This
implies a one-dimensional spectrum varying as
k
−
2
.
5
.
Additional detailed, quantitative studies of the nonlinear development of
the primary gradient drift theory have been reported by Sudan and Keskinen
2
and
(δ
n
/
n
)
(δ
E
)
Search WWH ::
Custom Search