ocean: wind-driven circulation #2• ocean transport to the right of the wind in nh. • ocean...
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![Page 1: Ocean: Wind-driven circulation #2• Ocean transport to the right of the wind in NH. • Ocean transport to the left of the wind in SH. • Ekman pumping & suction: • Convergence](https://reader035.vdocument.in/reader035/viewer/2022071507/612876c46e59013d44565ba5/html5/thumbnails/1.jpg)
Ocean: Wind-driven circulation #2
ATM2106
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Last time…
• Ekman layer : The layer near the surface that feels the wind stress
• Ekman transport : Wind drives ocean currents • Ocean transport to the right of the wind in NH. • Ocean transport to the left of the wind in SH.
• Ekman pumping & suction: • Convergence : Ekman pumping (downward) • Divergence : Ekman suction (upward)
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What does Ekman pumping do to the interior of the ocean?
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Remember that…
• Ekman pumping in the Ekman layer. • Beneath the Ekman layer, the flow is in the geostrophic
balance.
Geostrophic balance
w associated with Ekman pumping/suction
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Using momentum equations…
�fv = � 1
⇢ref
@p
@x
fu = � 1
⇢ref
@p
@y
@
@y(�fv) = � 1
⇢ref
@
@y
✓@p
@x
◆
@
@x(fu) = � 1
⇢ref
@
@x
✓@p
@y
◆
@
@y(�fv) =
@
@x(fu)
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Using momentum equations…
@
@y(�fv) =
@
@x(fu)
f = f0 + �y
If we assume that
�f@v
@y� �v = f
@u
@x
�f
✓@u
@x+
@v
@y
◆= �v
f@w
@z= �v
@u
@x+
@v
@y+
@w
@z= 0
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1. Ekman pumping
Ekman layer
f@w
@z= �v
w = 0
w = wEK
y
z
(wEK < 0)
Ekman pumping leads to v < 0 in the NH ( f > 0 ).
H
v =f
�
wEK
H
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1. Ekman suction
Ekman layer
f@w
@z= �v
w = 0
w = wEK
y
z
Ekman pumping leads to v > 0 in the NH ( f > 0 ).
H
(wEK > 0)
v =f
�
wEK
H
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Ekman pumping / suction
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How fast is v driven by Ekman pumping/suction?
v =f
�
wEK
H
1000 m2 x 10-11 m-1 s-1
1 x 10-4 s-1 30 m yr-1
v = O(1cm/s)
(Thermocline depth)
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The depth-integrated circulation
• To simplify the ocean circulation, let’s consider the vertical integration of the momentum equation.
fu+1
⇢ref
@p
@y=
1
⇢ref
@⌧y@z
�fv +1
⇢ref
@p
@x=
1
⇢ref
@⌧x@z
�f@v
@y� �v +
1
⇢ref
@2p
@x@y=
1
⇢ref
@
@z
✓@⌧x@y
◆
f@u
@x+
1
⇢ref
@2p
@x@y=
1
⇢ref
@
@z
✓@⌧y@x
◆
�v = f@w
@z+
1
⇢ref
@
@z
✓@⌧y@x
� @⌧x@y
◆
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The depth-integrated circulation
�v = f@w
@z+
1
⇢ref
@
@z
✓@⌧y@x
� @⌧x@y
◆
Z 0
�D�vdz =
Z 0
�Df@w
@zdz +
Z 0
�D
1
⇢ref
@
@z
✓@⌧y@x
� @⌧x@y
◆dz
�V =1
⇢ref
✓@⌧wind,y
@x� @⌧wind,x
@y
◆
Vertical integration
w(z=0) = w(z=-D) = 0⌧(z = �D) = 0
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Sverdrup relation
�V =1
⇢ref
✓@⌧wind,y
@x� @⌧wind,x
@y
◆
The depth-integrated meridional transport is determined by wind stress when we assume
1. Coriolis force, pressure gradient force and stress are balanced. 2. Homogeneous fluid (so density is constant) 3. No vertical flow at the surface and the bottom 4. Stress is zero at the bottom
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Sverdrup relation �V =1
⇢ref
✓@⌧wind,y
@x� @⌧wind,x
@y
◆
(+)
(+)
(−)
(−)
wind stress curl
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Wind stress curl, geostrophic current, Sverdrup relation
- Northern H. : poleward - Southern H. : equatorward
- Northern H. : equatorward - Southern H. : poleward
@⌧y@x
� @⌧x@y
> 0@⌧y@x
� @⌧x@y
< 0
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Sverdrup relation �V =1
⇢ref
✓@⌧wind,y
@x� @⌧wind,x
@y
◆
(+)
(+)
(−)
(−)
wind stress curl
No meridional transport
No meridional transport
No meridional transport
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Sverdrup relation �V =1
⇢ref
✓@⌧wind,y
@x� @⌧wind,x
@y
◆
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Why does it have to be on the west side?
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Green: eastward
brown: westward
Green: northward
brown: southward
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Schematic of surface circulation (modified from Schmitz, 1995)
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Stratified ocean and eddies
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Homogeneous ocean v.s. ocean with eddies
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Baroclinic instability
• Stratified ocean has tilted isopycnal (same density line).
• It means that there is available potential energy (APE).
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Available potential energy
• It is responsible for the atmospheric eddies.
• It is also responsible for the oceanic eddies.
• The stratified fluid with tilted isopycnal has higher potential energy than that with flat isopycnal.
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A schematic of the mechanism maintaining the tilt isopycnal
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Atmospheric eddies v.s. oceanic eddies
Atmospheric eddies Oceanic eddies
Length scale 700 km 50 km
Time scale 1 day A week
Source APE by radiative imbalance
Mechanically produced APE
Role Heat and momentum transport
Heat and momentum transport but less crucial
than those in the atmosphere