Geoscience Reference
In-Depth Information
SincewewereabletomeasureReynoldsstresswiththeADVstomuchlowerlev-
els than possible previously,we reasonedthat the ISPOL turbulencedata set might
provideguidanceindeterminingjusthowfarthe
z
-dependenceofmixinglengthex-
tendedin a similarity sense.With neutralstratificationthe maximummixinglength
shouldbe the smaller of
, dependingon whetherthe measurement
levelisinthesurfacelayerorouterlayer(wherewearemakingthetacitassumption
that the surface layer is defined as the region where mixing length varies with dis-
tancefromthe boundary).At67
◦
S,
Λ
∗
u
∗
/ |
f
|
or
κ
|
z
|
10
−
4
s
−
1
, andwithourestimateof
|
f
|
=
1
.
33
×
Λ
∗
=
0
.
028,formeasurementsmade4mfromtheboundary,
λ
wouldbethesmaller
of
u
∗
or 1.6m, where the tilde acknowledgesthat
u
∗
may differ somewhat
from
u
∗
0
. Ideally then, if we plotted
∼
200
×
λ
versus
u
∗
it should increase linearly until it
8mms
−
1
and then remain about constant for higher values. In other
words, for friction velocity values less than 8mms
−
1
, 4m is beyond the surface
layer and the planetary scale dominates, whereas for greater values, the geometric
scale
reached
u
∗
≈
rules.
For all of the 3-h turbulence samples during the first ISPOL deployment
(1-25December),weassembledascatterplotof
κ
|
z
|
u
w
+
λ
=
0
.
85
/
k
max
versus
u
∗
=
|
1
/
2
(Fig.5.7).Despitefairlylargesample-to-samplevariation,theregression
v
w
|
i
Fig. 5.7
Scatter plot of mixing length
versus
u
∗
for all 3-h averages prior to the ISPOL
Christmas-Day breakup. The heavy dot-dashed line is a least-squares linear fit through the origin
with 95% confidence interval indicated by the light dashed lines. The heavy dashed line indicates
the dynamic (planetary) maximum mixing length. The grey dashed lines indicate the “geomet-
ric” limits,
λ
κ
|
z
|
, at 2 and 4m, respectively (From McPhee 2008, in press) (see also Colorplate on