Geoscience Reference
In-Depth Information
AgainusingtheformalismintroducedinSection3.5,we have
T
−
1
[
U
z
]=
dependentquantity
−−−−−−−−−−
[
κ
z
]=
L
LT
−
1
[
u
∗
0
]=
governingparameters
w
b
0
=
L
2
T
−
3
Threegoverningparameters,twowithindependentdimensions,implythatadimen-
sionlessgroupincludingwindshear willbean asyetundeterminedfunctionofone
other dimensionless group, formed from powers of the governing parameters. The
parameterexponentsaredeterminedbysolving
w
b
0
=[
κ
p
1
p
2
z
]
[
u
∗
0
]
L
:2
=
p
1
+
p
2
T
:
−
3
=
p
2
whence
κ
w
b
0
u
∗
0
3
z
=
0
sothatthecounterpartof(4.1)whenbuoyancyfluxisimportantis
u
∗
0
=
φ
m
κ
=
φ
m
z
L
0
w
b
0
u
∗
0
3
φ
m
=
κ
zU
z
z
=
φ
m
(
ζ
)
(4.4)
where
L
0
is the Obukhovlengthbased on surface (interface)momentumand buoy-
ancyflux.If
L
0
ispositive(assuming
z
ispositivedisplacementfromtheboundary),
turbulenceissuppressedbybuoyancyand
vice versa
if
L
0
isnegative.
The form of
has been studied extensively for the atmospheric surface
layer.Forexample,Busingeretal.(1971)suggestedthefollowingempiricalformula
coveringabroadrangeofatmosphericconditionsobservedfroma32-mtowerover
flat terraininKansas
1
:
φ
m
(
ζ
)
1
+
.
≥
4
7
ζ
L
0
0
φ
m
(
ζ
)=
(4.5)
ζ
)
−
1
/
4
(
1
−
15
L
0
<
0
Lettau (1979) studied near-surface profiles in the stably stratified atmosphere
over the Antarctic ice cap and suggested that the dimensionless shear had some
curvature,i.e.
3
/
4
φ
(
ζ
)=(
1
+
5
ζ
)
L
0
≥
0
(4.6)
m
1
Note that data from even this relatively tall tower in the atmosphere would correspond to mea-
surements made withinabout thefirst meter of the IOBL.
