Ekman Transport

• Ekman transport is the direct wind driven transport of seawater

• Boundary layer process

• Steady balance among the wind stress, vertical eddy viscosity & Coriolis forces

• Story starts with Fridtjof Nansen [1898]

Fridtjof Nansen

• One of the first scientist-explorers

• A true pioneer in oceanography

• Later, dedicated life to refugee issues

• Won Nobel Peace Prize in 1922

Nansen’s Fram

• Nansen built the Fram to reach North Pole

• Unique design to be locked in the ice

• Idea was to lock ship in the ice & wait

• Once close, dog team set out to NP

Fram Ship Locked in Ice

1893 -1896 - Nansen got to 86o 14’ N

Ekman Transport

• Nansen noticed that movement of the ice-locked ship was 20-40o to right of the wind

• Nansen figured this was due to a steady balance of friction, wind stress & Coriolis forces

• Ekman did the math

Ekman Transport

Motion is to the right of the wind

Ekman Transport

• The ocean is more like a layer cake

• A layer is accelerated by the one above it & slowed by the one beneath it

• Top layer is driven by w

• Transport of momentum into interior is inefficient

Ekman Spiral

• Top layer balance

of w, friction &

Coriolis

• Layer 2 dragged forward by layer 1 & behind by layer 3

• Etc.

Ekman Spirals

• Ekman found an exact solution to the structure of an Ekman Spiral

• Holds for a frictionally controlled upper layer called the Ekman layer

• The details of the spiral do not turn out to be important

Ekman Layer

• Depth of frictional influence defines the Ekman layer

• Typically 20 to 80 m thick

– depends on Az, latitude, w

• Boundary layer process

– Typical 1% of ocean depth (a 50 m Ekman layer

over a 5000 m ocean)

Ekman Transport

• Balance between wind stress & Coriolis force for an Ekman layer

– Coriolis force per unit mass = f u

• u = velocity

• f = Coriolis parameter = 2 sin

= 7.29x10-5 s-1 & = latitude

• Coriolis force acts to right of motion

Ekman Transport

Coriolis = wind stress

f ue = w / ( D)

Ekman velocity = ue

ue = w / ( f D)

Ekman transport = Qe

Qe = w / ( f) = [m2 s] = [m3 s-1 m-1]

(Volume transport per length of fetch)

Ekman Transport

• Ekman transport describes the direct wind-driven circulation

• Only need to know w & f (latitude)

• Ekman current will be right (left) of wind in the northern (southern) hemisphere

• Simple & robust diagnostic calculation

Current Meter Mooring

Current Meter Mooring

LOTUS

Ekman Transport Works!!

• Averaged the velocity profile in the downwind coordinates

• Subtracted off the “deep” currents (50 m)

• Compared with a model that takes into account changes in upper layer stratification

• Price et al. [1987] Science

Ekman Transport Works!!

Ekman Transport Works!!

theory

observerd

Ekman Transport Works!!

• LOTUS data reproduces Ekman spiral & quantitatively predicts transport

• Details are somewhat different due to diurnal changes of stratification near the sea surface

Inertia Currents

• Ekman dynamics are for steady-state conditions

• What happens if the wind stops?

• Ekman dynamics balance wind stress, vertical friction & Coriolis

• Then only force will be Coriolis force...

Inertial Currents

• Motions in rotating frame will veer to right

• Make an inertial circle

• August 1933, Baltic Sea, ( = 57oN)

• Period of oscillation is ~14 hours

Inertial Currents

• Inertial motions will rotate CW in NH & CCW in the SH

• These “motions” are not really in motion

• No real forces only the Coriolis force

Inertial Currents

• Balance between two “fake” forces

– Coriolis &

– Centripetal forces

Inertial Currents

• Balance between centripetal & Coriolis force

– Coriolis force per unit mass = f u

• u = velocity

• f = Coriolis parameter = 2 sin

= 7.29x10-5 s-1 & = latitude

– Centripetal force per unit mass = u2 / r

– fu = u2 / r -> u/r = f

Inertial Currents

• Inertial currents have u/r = f

• For f = constant

– The larger the u, the larger the r

– Know size of an inertial circle, can estimate u

• Period of oscillation, T = 2r/u (circumference of

circle / speed going around it)

– T = 2r/u = 2 (r/u) = 2 (1/f) = 2 /f

Inertial Period

• f = 2 sin()

• For = 57oN,

f = 1.2x10-4 s-1

• T = 2 / f = 51,400

sec = 14.3 hours

• Matches guess of 14 h

Inertial Oscillations

D’Asaro et al. [1995] JPO

Inertial Currents• Balance between Coriolis & centripetal forces

• Size & speed are related by value of f - U/R = f

– Big inertial current (U) -> big radius (R)

– Vice versa…

• Example from previous slide - r = 8 km & = 47oN

– f = 2 sin(47o) = 1.07x10-5 s-1

– U = f R ~ 0.8 m/s

– Inertial will dominate observed currents in the mixed layer

Inertial Currents

• Period of oscillations = 2 / f

– NP = 12 h; SP = 12 h; SB = 21.4 h; EQ = Infinity

• Important in open ocean as source of shear at base of mixed layer

– A major driver of upper ocean mixing

– Dominant current in the upper ocean