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In-Depth Information
speculate that the lockstep variations in proxy temperature and CO
2
from air bub-
bles trapped in the Vostok ice core spanning several glacial maxima and minima
(Petit et al. 1999) result from interaction between the physics of deep convection
in the Southern Ocean and other elements of the global carbon cycle (Sigman and
Boyle2000).
In both the Arctic and Antarctic, understanding how sea ice interfaces with the
ocean through the medium of the IOBL is key to determining how polar regions
interactwith theclimate. Asimpliedabove,theformthatinteractiontakesdepends
strongly on the exchange of heat, salt and momentum at the immediate ice/ocean
boundary;thedensitystructureofthewatercolumn;andhowthosefactorsinfluence
scalesofturbulencein theIOBL.
1.3 Ekman's Seminal Paper
Any work on the IOBL footnotes to a remarkable paper published (the English
version) in 1905 by V. W. Ekman, a Swedish oceanography student who worked
with V. Bjerknes and F. Nansen on a mathematical theory to explain Nansen's
observations that the
Fram
, on its famous 1893-1896 expedition in the Arctic
Ocean,oftendriftedtotherightofthesurfacewind.Intheintroductiontothepaper,
Ekmanwrote
On studying the observations of wind and ice-drift taken during the drift of the FRAM,
Fridtjof Nansen found that the drift produced by a given wind did not, according to the
general opinion,followthewind'sdirectionbutdeviated 20
◦
-40
◦
totheright.Heexplained
this deviation as an obvious consequence of the earth's rotation; and he concluded further
that thewater-layer immediatelybelow thesurface must haveasomewhat greater deviation
than thelatter and so on, since every water-layer isput in motionby thelayer immediately
above, sweeping over itlikeawind
...
Hethenproceededtodevelopanevenmoreelegantmathematicaldescriptionofthe
processdescribedinhisprose,culminatinginthefamousspiralstructureinrotating
boundarylayersnownamedafterhim.Inmodernnotation,hissolutiontothesteady
stateequationsforaboundarylayerinarotatingreferenceframe(Chapter2)maybe
written in terms of a complex number representing a two-dimensional (horizontal)
velocityvector:
V
=
V
x
e
x
+
V
y
e
y
=
V
r
+
iV
i
:
1
/
2
1
/
2
τ
0
e
(
f
/
2
K
)
(
1
+
i
)
z
V
(
z
)=(
i
/
fK
)
(1.1)
where
f
is theCoriolisparameter(twicethe localverticalrotationrate),
K
is“eddy
viscosity”;
τ
0
is kinematic stress at the boundary, and
z
is positive upward (nega-
tiveintheocean).Ekmannotedthatattheboundary
(
z
=
0
)
,thevelocityandstress
/
√
2
e
i
π
/
2
1
/
2
are related by a factor containing the term
which ro-
tates surface velocity 45
◦
to the right of surface stress in the northern hemisphere,
qualitatively explaining Nansen's observations. The exponentialterm in (1.1) both
(
)
=(
1
)(
1
+
i
)
