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Ekman Transport

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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  1. 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]

  2. 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

  3. 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

  4. Fram Ship Locked in Ice

  5. 1893 -1896 - Nansen got to 86o 14’ N

  6. 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

  7. Ekman Transport Motion is to the right of the wind

  8. 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

  9. Ekman Spiral • Top layer balance of tw, friction & Coriolis • Layer 2 dragged forward by layer 1 & behind by layer 3 • Etc.

  10. 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

  11. 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)

  12. 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

  13. 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)

  14. 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

  15. Current Meter Mooring

  16. Current Meters Vector Measuring Vector Averaging Current Meter Current Meter

  17. Current Meter Mooring

  18. LOTUS

  19. 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

  20. Ekman Transport Works!!

  21. Ekman Transport Works!! theory observerd

  22. 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

  23. 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...

  24. 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

  25. 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

  26. Inertial Currents • Balance between two “fake” forces • Coriolis & • Centripetal forces

  27. 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

  28. 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

  29. 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

  30. Inertial Oscillations D’Asaro et al. [1995] JPO

  31. 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

  32. 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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