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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
 
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