Ocean: wind-driven circulation
ATM2016
Last time
• Ocean circulation
• Hydrostatic balance
• Geostrophic balance
• Thermal wind relationship
• Sea level and isopycnal (lines with the same density)
Today
• Wind stress
• Wind-driven circulation
• Ekman transport
• Upwelling / Downwelling
• Ekman pumping
• Convergence / divergence
Averaged wind speed
Averaged wind stress
Wind and wind stress
Wind = wind stress ?
Weak stress
Wind and wind stress
Moderate stress
Wind = wind stress ?
Wind and wind stress
Strong stress
Wind = wind stress ?
Wind and wind stress
Wind stress = cD ρair |uair - uwater| (uair - uwater)
Crag coefficient
Wind stress ∝ uair2
How does the ocean feel the wind stress?
Fx =1
⇢ref
@⌧x@z
Fy =1
⇢ref
@⌧y@z
How does the ocean feel the wind stress?
Wind stress decreases rather rapidly with depth.
Ekman layer
Dynamics in the Ekman layer
�fv +1
⇢ref
@p
@x=
1
⇢ref
@⌧x@z
�f(vg + va) +1
⇢ref
@p
@x=
1
⇢ref
@⌧x@z
�fva =1
⇢ref
@⌧x@z
�fv +1
⇢ref
@p
@x= Fx
Dynamics in the Ekman layer
�fva =1
⇢ref
@⌧x@z
fua =1
⇢ref
@⌧y@z
f⇢ref
Z 0
��uadz = ⌧y,wind
�f⇢ref
Z 0
��vadz = ⌧x,wind
Dynamics in the Ekman layer
f⇢ref
Z 0
��uadz = ⌧y,wind
�f⇢ref
Z 0
��vadz = ⌧x,wind
WindW
ind
Ocean currentO
cean
cur
rent
North hemisphere
• Transport of the water in the Ekman layer is to the right of the wind stress direction in the northern hemisphere
• Transport of the water in the Ekman layer is to the left of the wind stress direction in the southern hemisphere.
• Ekman spiral
Dynamics in the Ekman layer
Ekman spiral
Wind stress structure
Wind stress structure
@⌧x@y
> 0@⌧x@y
< 0
- Northern H. : divergence - Southern H. : convergence
- Northern H. : convergence - Southern H. : divergence
Wind stress structure
@⌧y@x
< 0@⌧y@x
> 0
- Northern H. : divergence - Southern H. : convergence
- Northern H. : convergence - Southern H. : divergence
Wind stress structure
- Northern H. : divergence - Southern H. : convergence
- Northern H. : convergence - Southern H. : divergence
@⌧y@x
� @⌧x@y
> 0@⌧y@x
� @⌧x@y
< 0
Wind stress structure
Sea level
Ekman pumping / suction
Anticyclonic applied stress
Cyclonic applied stress
Convergenceand
Downwelling
Divergenceand
Upwelling
Ekman pumping / suction
Ekman pumping at the equator
Ekman pumping / suction and temperature