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

Nansen got to 86 o 14’ N

Ekman Transport Nansen noticed that movement of the ice- locked ship was o 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 A z, 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 u e =  w / (  D) Ekman velocity = u e u e =  w / (  f D) Ekman transport = Q e Q e =  w / (  f) = [m 2 s] = [m 3 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

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!!

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, (  = 57 o N) 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 = u 2 / r – fu = u 2 / 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 = 2  r/u (circumference of circle / speed going around it) – T = 2  r/u = 2  (r/u) = 2  (1/f) = 2  /f

Inertial Period f = 2  sin(  ) For  = 57 o N, 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 &  = 47 o N –f = 2  sin(47 o ) = 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