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2
T
∂ξ
i
K
∗
=
∂
T
(4.10)
2
withboundaryconditionsfortheIOBL(with
z
positiveupward)
T
(
0
)=
1
T
(
−
∞
)=
0
andsolutionsimply
e
δ
ξ
T
=
(4.11)
where
1
/
2
δ
=(
±
i
/
K
∗
)
(4.12)
wherethesignpreceding
i
dependsonthehemisphere(
northern).Theexponential
argument is complex, meaning that it both rotates and attenuates stress as depth
increases(Fig.4.3);i.e.,theEkmanspiralpertainstostress aswell asvelocity.
The problem is formulated here in terms of stress rather than velocity since
almostbydefinition,thereislittlevariationinstresswithintherelativelythinsurface
layer,andwecansurmisethatneartheboundarytheReynoldsstressspiralisinsen-
sitivetovariationineddyviscosity.Thiscontrastswith thestrongshearapparentin
thevelocityprofile.SignificantturningintheReynoldstractionvectorwithincreas-
ingdepthhasbeenobservedrepeatedlyduringicestationexperiments.Anexample
is illustrated by measurements (Fig. 4.4) from the Ice Station Weddell experiment
(McPhee and Martinson 1994). During a storm that lasted about two days, strong
southerly winds blew the station northward, setting up a well developed and rela-
tively steady IOBL. We calculated zero-lag covariance of vertical with horizontal
velocitycomponentsforeach15-minflow realization,thenaveragedthese overthe
course of the storm to get mean kinematic stress estimates at 5 levels rangingfrom
4 to 24m below the ice/water interface. Results clearly show substantial leftward
deflectionandattenuationoftheReynoldsstresswithincreasingdepth.
ThespiralprofileshowninFig.4.4isfrom
+
u
∗
0
u
∗
0
exp
1
u
∗
0
√
2
K
∗
(
τ
(
z
)=
1
−
i
)
|
f
|
z
/
(4.13)
ξ
= 0
ξ
=
-
0.5
ξ
=
-
0.1
ξ
=
-
0.2
Fig. 4.3
The nondimensional stress profile illustratingtheEkman stress spiral
