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 icelocked 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 tw
• Transport of momentum
into interior is inefficient
Ekman
Spiral
• Top layer balance of
tw, 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, tw
• 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 W sin f
W = 7.29x10-5 s-1 & f = latitude
• Coriolis force acts to right of motion
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)
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
Current Meter Mooring
Current Meters
Vector Measuring
Current Meter
Vector Averaging
Current Meter
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,
(f = 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 W sin f
W = 7.29x10-5 s-1 & f = 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 = 2pr/u
(circumference of circle / speed going around it)
– T = 2pr/u = 2p (r/u) = 2p (1/f) = 2p /f
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
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 & 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
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