Upper ocean currents, Coriolis force, and Ekman Transport

Gaspard-Gustave de CoriolisWalfrid Ekman

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

Seasonal input o

f new

nutrients

from winter

convection

Time scales greater than

a day introduce earth’s

rotation in the dynamics –

Coriolis force

Fro

m L

alli

and

Par

son,

“B

iolo

gica

l Oce

anog

raph

y”

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.

In the Northern Hemisphere the local rotation is counter-clockwise, and Coriolis force deflects motion to the right.

N

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 275-300) 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).

In the Northern hemisphere …

Earth’s rotation is counter clockwise …

and Coriolis force is to the right …

of the direction of movement

Coriolis force

dire

ctio

n of

flo

w

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 directionof movement

So direction of movementis to the right of the wind (in the northern hemisphere)

Wind force Coriolis force

Cur

rent

Win

d fo

rce

Current

Win

d fo

rce

Current

Wind force

Current

Wind force

Current

DE

DE

• 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)

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.)

windwind

water

Eastern Boundary Current program Progressive vector diagram. Apr-Oct 1993

Equator-ward winds on ocean eastern boundaries

Pole-ward wind on ocean western boundaries

Pole-ward winds on ocean eastern boundaries

Equator-ward wind on oceanwestern boundaries

http://marine.rutgers.edu/cool/research/upwelling.html

Wind

forc

e

Current

The magnitude of the Ekman transport is

m2 s-1

τ = wind stress (Pascals or N m-2) = 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 and along-shelf currents at various depths along the continental shelf off northwest Africa

W

ind

sp

ee

d m

s-1

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

3 4 1/ 0.7 /(15 10 ) 0.5 10

x Ekman

Ekman x

w L U

w U L x x ms

Wind data show southerly of 6 m s-1 over a few days

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.

Over 1 day (86400 sec) this is 4.32 m day-1

Dep

th (

z)

uE

Dep

th (

z)

Dep

th (

z)

fDE

2

uE

Dep

th (

z)

Typical τ= 0.1 Pa

f = 5x10-5 at 20N

typical DE ~ 30 m

uE ~ 0.1 / 1027 / 5x10-5 / 30 = 6.5 cm s-1

Northwest Africa values:

50/8 = 6.25 km day-1typical τ= 0.1 Pa

f = 5x10-5 at 20N, DE ~ 30 m

= 5.6 km/day

Alongshore flowshaded into page

i.e. poleward

Across-shore flowshaded to left (offshore)

Density(kg m-3)

6 cm/s

Upwelling favorable wind is out of the page

Wind-driven currents and upwellingOn 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