Transcript Coriolis force and Ekman transport

Upper ocean currents, Coriolis force,
and Ekman Transport
Walfrid Ekman
Gaspard-Gustave de Coriolis
Upper ocean currents, Coriolis force,
and Ekman Transport
• In the open ocean mixed layer: vertical structure was the
key to biological productivity
– mixing, light, stratification, critical depth
• In coastal regions and the equator, wind-driven
horizontal currents can cause upwelling of water with
high nutrients leading to sustained production over a
season, or longer
– Wind stress + Coriolis force give…
Ekman currents and upwelling
From Lalli and Parson, “Biological Oceanography”
Some physics…
Coriolis force:
In a fixed frame of reference the ball travels in
a straight line (Newton’s laws)
In a rotating frame of reference (on the table,
or Earth), the ball appears to turn.
In the example, the merry-go-round is turning
clockwise and the ball turns toward the left.
This is the Southern Hemisphere effect.
N
In the Northern Hemisphere the local rotation
is counter-clockwise, and Coriolis force
deflects motion to the right.
S
http://marine.rutgers.edu/dmcs/ms320/coriolis.mov
Handout-Coastal-Upwelling.pdf
Figure 9.1 Inertial currents in the North Pacific in October 1987 (days 275300) measured by holey-sock drifting buoys drogued at a depth of 15
meters. Positions were observed 10-12 times per day by the Argos system
on NOAA polar-orbiting weather satellites and interpolated to positions every
three hours. The largest currents were generated by a storm on day 277.
Note: these are not individual eddies. The entire surface is rotating. A
drogue placed anywhere in the region would have the same circular motion.
From van Meurs (1998).
Earth’s rotation is counter clockwise …
and Coriolis force is to the right …
of the direction of movement
direction of flow
In the Northern hemisphere …
Coriolis force
In the absence of any
other forces, Coriolis
drives clockwise (NH)
rotating inertial
oscillations
Suppose a balance of forces
between wind stress and Coriolis
Coriolis force is to right of the direction
of movement
Coriolis force
Current
Wind force
Current
Wind force
So direction of movement
is to the right of the wind
(in the northern hemisphere)
Wind force
Current
Wind force
Current
DE
DE
æp p
u = V0 cosç +
è 4 DE
ö p z DE
z÷ e
ø
æp p
v = V0 sinç +
è 4 DE
ö p z DE
z÷ e
ø
• V0 is 45° to the right of the wind (in the northern hemisphere)
• V0 decreases exponentially with depth as it turns clockwise (NH)
• At depth z = -DE the flow speed falls to e-π = 0.04 times the surface
current and is in the opposite direction (typical DE is 20 to 40 m)
Eastern Boundary Current program Progressive vector diagram. Apr-Oct 1993
water
wind
Progressive vector diagram, using daily averaged currents relative to the flow at 48 m, at a
subset of depths from a moored ADCP at 37.1°N, 127.6°W in the California Current,
deployed as part of the Eastern Boundary Currents experiment. Daily averaged wind
vectors are plotted at midnight UT along the 8-m relative to 48-m displacement curve. Wind
velocity scale is shown at bottom left. (From: Chereskin, T. K., 1995: Evidence for an Ekman balance
in the California Current. J. Geophys. Res., 100, 12727-12748.)
Equator-ward winds on ocean
eastern boundaries
Pole-ward winds on ocean
eastern boundaries
Pole-ward wind on ocean
western boundaries
Equator-ward wind on ocean
western boundaries
http://marine.rutgers.edu/cool/research/upwelling.html
The magnitude of the Ekman transport is
t
UE =
rf
m2 s-1
τ = wind stress (Pascals or N m-2)
r = water density (1027 kg m-3)
f = Coriolis parameter = 2 Ω sin φ
Ω = 2π/(24 hours)
= 2 x Earth rotation rate x sin(latitude)
Wind speed m s-1
Wind speed and along-shelf currents at various depths along the
continental shelf off northwest Africa
Strong wind toward south
Weak or no wind
Wind-driven currents and upwelling
On timescales longer than a few days:
Earth’s rotation introduces Coriolis force
•
flow turns to the right (northern
hemisphere) or
left (southern hemisphere)
•
wind stress balances Coriolis force =
Ekman transport
Oceanographer’s rule:
Ekman transport is toward
the right of the wind stress
(in northern hemisphere)
Adjacent to a coast…
Alongshore wind produces Ekman transport across-shore …
causes upwelling or downwelling of a few meters per day
Estimating the upwelling velocity from NJ coast data
Wind data show southerly of 6 m s-1 over a few days
2
t = rair CDuwind
= (1.3)(1.6x10 -3 )(62 ) = 0.07 Pa
U Ekman =
t
= (0.07) / (1000 *10-4 ) = 0.7 m2 s -1
rf
To balance mass transport in a 2-dimensional (across-shelf/vertical) process, the
average upwelling velocity (w) times the width of the upwelling zone must balance
the Ekman transport.
w Lx  U Ekman
w  U Ekman / Lx  0.7 /(15 x103 )  0.5 x104 ms 1
Over 1 day (86400 sec) this is 4.32 m day-1
Depth (z)
Depth (z)
Depth (z)
uE
t
UE =
= average velocity ´ depth
rf
Depth (z)
uE
Northwest Africa values:
Typical = 0.1 Pa
2
DE 
f
UE
t
2u t
1
uE =
=
/
=
DE r f
f
r 2u f
f = 5x10-5 at 20N
typical DE ~ 30 m
uE ~ 0.1 / 1027 / 5x10-5 / 30 = 6.5 cm s-1
typical = 0.1 Pa
f = 5x10-5 at 20N, DE ~ 30 m
uE =
UE
0.1
1
-1
=
=
6.5cm
s
DE (1027)(5x10 -5 ) 30
= 5.6 km/day
Upwelling favorable
wind is out of the page
Alongshore flow
shaded into page
i.e. poleward
Across-shore flow
shaded to left (offshore)
s = r - 1000
Density
(kg m-3)
6 cm/s
Wind-driven currents and upwelling
On timescales longer than a few days:
Earth’s rotation introduces Coriolis force
•
flow turns to the right (northern
hemisphere) or
left (southern hemisphere)
•
wind stress balances Coriolis force =
Ekman transport
Oceanographer’s rule:
Ekman transport is toward
the right of the wind stress
(in northern hemisphere)
Adjacent to a coast…
Alongshore wind produces Ekman transport across-shore …
causes upwelling or downwelling of a few meters per day