Geoscience Reference
In-Depth Information
Figure 12.6 An acoustic sounder record from a nocturnal SBL with strong gravity
waves. Photo courtesy W. D. Neff. From
Wyngaard
(
1988
).
a
t
involves both phase and
ensemble averaging. The phase averaging is defined through
a
w
The decomposition of a variable
a
˜
=
A
+
+
1
N
nτ )
N
a
p
a
w
,
˜
=
lim
N
1
˜
a(t
+
=
A
+
(12.23)
→∞
n
=
since the phase average of
a
t
is zero. Under stationary conditions a time average
converges to the ensemble average, so in practice one determines the mean part
A
through
T
1
T
A
=
lim
a(t) dt.
˜
(12.24)
T
→∞
0
˜
Thus, taking the time average of
a
gives its mean part
A
; subtracting the mean
a
gives the wave part
a
w
; and subtracting the phase
A
from the phase average of
average
A
+
a
w
from
a
gives the turbulent part
a
t
.
The averaging rules (
Finnigan
et al
.
,
1984
)are
(a
t
)
p
a
t
a
w
=
0
,
=
0
,
=
0
,
(a
w
b)
p
a
w
b
p
,
(ab)
p
ab
p
,
=
=
=
ab
ab,
a
p
=
(a
w
b
t
)
p
=
a,
a
p
=
a,
a
w
b
t
=
0
.
(12.25)
