Geoscience Reference
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height of z
D, the current is deflected to left of the upper layer flow. This deflection of
the near-bed flow, known as Ekman veering, is widely observed in the ocean although it
is generally less than indicated by our simple model with typical values 5
¼
15
(Kundu,
1976
; Weatherly and Martin,
1978
). Veering also occurs in the atmosphere and is
apparent in weather charts as a deflection of the surface wind relative to the isobars.
It is apparent in
Fig. 3.9
that there is a component of transport in the positive
y direction. Integrating
Equation (3.47)
, we find this net transport to have the
simple form:
∼
1
1
u
g
D
2
u
g
e
z
=
D
sin
¼
ð
=
Þ
¼
:
ð
3
:
48
Þ
vdz
z
D
dz
0
0
This flow perpendicular to the high level current can be thought of as the result of
the weakening of the bottom current by boundary friction leaving an unbalanced
component of the pressure gradient which drives the cross-stream flow. We shall see
in
Chapter 10
that this transverse flow in the bottom boundary layer can play a major
part in downslope transport at the shelf edge where, outside the boundary layers, the
flow is constrained to be parallel to the depth contours.
3.5.3
Response to the Ekman transport at a coastal boundary
Our derivation of the Ekman transport is based on the assumption that there are no
horizontal pressure gradients, which is reasonable in the open ocean. Near to the
coast, however, there can be no transport normal to the coastal boundary and so
pressure gradients will develop in response to either onshore or offshore Ekman
transport. Imagine a wind blowing parallel to the shore in the northern hemisphere
with the land to the right of the wind direction. In this case the Ekman transport will
be towards the coast and will act to pile up water against the coast, thus raising sea
level and producing an opposing pressure gradient. As a result of this pressure
gradient there will be a tendency for water to downwell at the coast and return
seawards in the lower layers if the water is deeper than the thickness of the Ekman
layer. Conversely, if the wind is in the opposite direction, surface water will move
offshore, sea level will fall at the coast and the pressure gradient will act to promote
onshore flow in the lower layers with upwelling of water near the coast. We shall
examine the dynamics of response to wind forcing in these situations, starting with
the simplest one-layer model.
One-layer model of the barotropic response
Consider the case where the transport is onshore as in
Fig. 3.10a
. We shall assume
that the coast is straight, that the density r is constant and that conditions are
uniform in the y (northward) direction. The flow is further assumed to be independ-
ent of depth, so we seek a solution of the linearised, vertically averaged equations of
motion. Setting Du/Dt
t etc. in
Equations (3.13)
, integrating over depth and
applying our assumptions, we have for the dynamical equations:
¼ @
u/
@
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