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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

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Ekman Transport

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Ekman transport l.jpg

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]


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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


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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


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Fram Ship Locked in Ice


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1893 -1896 - Nansen got to 86o 14’ N


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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


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Ekman Transport

Motion is to the right of the wind


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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 tw

  • Transport of momentum into interior is inefficient


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Ekman Spiral

  • Top layer balance of tw, friction & Coriolis

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

  • Etc.


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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


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Ekman Layer

  • Depth of frictional influence defines the Ekman layer

  • Typically 20 to 80 m thick

    • depends on Az, latitude, tw

  • Boundary layer process

    • Typical 1% of ocean depth (a 50 m Ekman layer over a 5000 m ocean)


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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 W sin f

        W = 7.29x10-5 s-1 & f = latitude

  • Coriolis force acts to right of motion


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Ekman Transport

Coriolis = wind stress

f ue = tw / (r D)

Ekman velocity = ue

ue = tw / (r f D)

Ekman transport = Qe

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

(Volume transport per length of fetch)


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Ekman Transport

  • Ekman transport describes the direct wind-driven circulation

  • Only need to know tw & f (latitude)

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

  • Simple & robust diagnostic calculation


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Current Meter Mooring


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Current Meters

Vector Measuring Vector Averaging

Current Meter Current Meter


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Current Meter Mooring


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LOTUS


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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


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Ekman Transport Works!!


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Ekman Transport Works!!

theory

observerd


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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


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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...


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Inertial Currents

  • Motions in rotating frame will veer to right

  • Make an inertial circle

  • August 1933, Baltic Sea, (f = 57oN)

  • Period of oscillation is ~14 hours


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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


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Inertial Currents

  • Balance between two “fake” forces

    • Coriolis &

    • Centripetal forces


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Inertial Currents

  • Balance between centripetal & Coriolis force

    • Coriolis force per unit mass = f u

      • u = velocity

      • f = Coriolis parameter = 2 W sin f

        W = 7.29x10-5 s-1 & f = latitude

    • Centripetal force per unit mass = u2 / r

    • fu = u2 / r -> u/r = f


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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 = 2pr/u (circumference of circle / speed going around it)

    • T = 2pr/u = 2p (r/u) = 2p (1/f) = 2p /f


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Inertial Period

  • f = 2 W sin(f)

  • For f = 57oN, f = 1.2x10-4 s-1

  • T = 2 W / f = 51,400 sec = 14.3 hours

  • Matches guess of 14 h


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Inertial Oscillations

D’Asaro et al. [1995] JPO


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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 & f = 47oN

    • f = 2 W sin(47o) = 1.07x10-5 s-1

    • U = f R ~ 0.8 m/s

    • Inertial will dominate observed currents in the mixed layer


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Inertial Currents

  • Period of oscillations = 2 p / 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


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