Geoscience Reference
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V
s
u
∗
0
=
1
κ
(
U
0
=
log
Ro
∗
−
A
∓
iB
)
(4.19)
wherethesignoftheimaginarytermdependsonthehemisphere(negativefornorth-
ern).Thisrelatesthe totalchangein(vector)velocityacrossthe IOBLto thevector
frictionvelocityattheboundary,providedthewellmixedlayerisnotshallowcom-
pared with the depth to which turbulence is active, and boundary buoyancy flux is
small(
L
0
large).
Theimaginarypartof(4.19)isconstantandprovidesguidanceforestimatingthe
valueofthesimilarity parameter
Λ
∗
from
κ
√
2
Λ
∗
2
B
=
Λ
∗
+
(4.20)
κ
2
From results of a wind/free-drift analysis of AIDJEX data, we estimated (McPhee
1981) that
B
≈
2
.
1 which implies
Λ
∗
=
.
024. The corresponding value for
A
is
then about 2.3. It should be noted that atmospheric estimates of
B
obtained by
comparing geostrophic wind aloft with surface friction velocity are often consid-
erably higher. But these analyses depend on friction velocity measured near typi-
cally smoothboundaries,thus ignoringtheimpactof largerroughnessfeaturesthat
mightaffectgeostrophicdrag,andalso donotconsidertheimpactofrelativelylow
inversionheights.Still, thevaluederivedfromtheAIDJEXanalysisshouldbecon-
sideredonlyapproximate.We havefoundfromanalyzingandmodelingIOBL data
fromseveraldifferentsourcesthatareasonablevalueisslightlylarger:
0
028,
but acknowledge that this could easily depart from the “true” constant by as much
as10-15%.
In terms of a customary quadratic drag relationship,
Λ
∗
=
0
.
c
g
V
s
the drag coef-
|
τ
0
|
=
U
−
0
butaccordingto(4.19),dragdoesnotfollowastrictly quadratic
power relation—in fact, the exponent in the relation
ficientis
c
g
=
V
s
was close to
n
7
rather than 2, for the AIDJEX stations in free drift (McPhee 1979). For a typical
sea-iceundersurfaceroughnessof0.03m,with
A
τ ∝
=
1
.
1,thedragcoef-
ficient magnitude and turning angle for ice speeds ranging from 0.05 to 0
=
2
.
3and
B
=
2
.
5ms
−
1
.
areplottedin Fig.4.6.
4.2.3 Similarity for the Stably Stratified IOBL
When there is stabilizing buoyancy flux from ice melting, the vertical scales of
turbulence are reduced by gravitational force, and mixing is confined to shallower
depthsthan for neutralstability. Thishas two importanteffects. First, fresherwater
will begin to form a new pycnocline within the well mixed layer that existed when
melting began. This may inhibit subsequent mixing below its newly established
level, and we find that in the central Arctic, seasonal pycnoclines generally form
by mid-to-late July as meltwater mixes into the upper ocean. Second, by confining
momentum transfer to a shallower layer, it will reduce effective drag on the ice
