ekman transport ekman transport is the direct wind driven transport of seawater boundary layer...
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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
• 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