Geoscience Reference
In-Depth Information
hemisphere so that at z
D the current is reversed in the direction relative to the
surface. At the surface, the u and v components are equal and positive so the flow is at
an angle of p/4 to the right (northern hemisphere) of the wind direction, a result that
was in qualitative agreement with Nansen's iceberg observations.
Projecting the tip of the current vector at each level into the horizontal plane
generates the famous Ekman spiral pattern, shown as the continuous curve in
Fig. 3.8 . This idealised form of flow has rarely been observed, partly because of the
difficulty of measuring currents in the near-surface layers of the ocean, but also
because the strong assumptions of the Ekman calculation are not usually satisfied.
In particular the eddy viscosity is probably far from constant, especially if the ocean
has varying stratification.
One very important result of Ekman's theory, which is independent of N z ,concerns
the vertically integrated transport. If we return to Equations (3.39) and assume that
h
¼
>>
D so that t x ¼
t y ¼
0atz
¼
h, then integration with respect to z gives:
f ð
ð
0
0
1
0
@
t x
@
t w
0
vdz
¼
fV
¼
z dz
¼
h
h
ð
3
:
43
Þ
f ð
ð
0
0
1
0
@
t y
@
udz
¼
fU
¼
z dz
¼
0
:
h
h
This means that the integrated volume transport is entirely in the y direction (i.e.
perpendicular to the wind stress) and has magnitude, referred to as the Ekman
transport,ofV
t w /r 0 f (units: m 2 s 1 ). This fundamental result on wind driven
transport expresses the fact that the wind stress at the surface is balanced by the
Coriolis force summed over depth. In order that the resultant Coriolis force opposes
the wind stress, the flow integrated over depth must be at right angles to the wind
direction. This Ekman transport in response to wind forcing plays a major role in
ocean circulation and underpins many conceptual models of the processes operating
in the upper ocean.
¼
3.5.2
The bottom Ekman layer
Currents near the seabed involve frictional stresses which result in a bottom layer
structure closely analogous to that occurring in the surface layer. In this case the
stresses are not forced externally but arise from the drag of the bottom boundary
on the near-bed flow. As an example of the dynamics in the bottom layer, consider
a steady flow u g which, well away from the bottom boundary, is directed in the
x direction and is in geostrophic balance, i.e.
0 @
1
p
fu g ¼
y :
ð
3
:
44
Þ
@
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