Ekman Transport

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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

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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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Nansens 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 -gt 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
DAsaro 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) -gt 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