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