Geoscience Reference
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attenuates velocity magnitude with increasing depth and rotates it clockwise (
cum
sole
) relative to the surface. At the depth
d
E
=
π
2
f
, the velocity is (somewhat
counterintuitively)oppositethesurfacevelocity.By carefulreasoning,Ekmanused
this to infer values for
K
, and showed that it must be several orders of magnitude
greaterthanmolecularkinematicviscosity.
Although there was much indirect evidence for
cum sole
deflection of currents
in both atmospheric and oceanic boundarylayers, the first unequivocalexample of
an Ekman spiral was published by Hunkins (1966), who used a composite of cur-
rentprofilesmeasuredoveratwo-monthperiodatArcticDriftStationAlphaduring
the International Geophysical Year in 1958 to fit an Ekman spiral starting a short
distance below the ice/water interface, where the current (relative to geostrophic
flow in the ocean) was 45
◦
degrees from the interfacial stress. He inferred an eddy
viscosity of about 0
0024m
2
s
−
1
from the relatively small currents he measured.
Ekmanhad suggestedwith remarkableinsight(basedpartly on the setup of coastal
currents during storms) that the eddy viscosity would depend on the square of the
surfacewindspeed,i.e.,onsurfacestress.Inafootnote,hesuggestedthateddyvis-
cositywouldberoughly0
.
0200m
2
s
−
1
inawindof7ms
−
1
,anorderofmagnitude
greaterthanHunkins'sestimate, whichwasbasedonweak meancurrentsobserved
fromice.Nevertheless,thelatterbecamea
de facto
standardforoceanographersfor
sometime,apparentlyforlackofotherdefinitivemeasurements.Asdescribedlater,
we now know that in essence Ekman got it right, and came very close to outlining
thesimilarityconceptsdiscussedin Chapter4.
ThereisagreatdealmoreinEkman's(1905)paperthanderivationofthesteady-
state Ekman spiral. With credit to Fredholm, he also presented a solution to the
time-dependentproblemandshowedthat circularcurrentsoscillatingwith aperiod
of a “half-pendulum day” (12h at the poles) about the mean currents would be
expected in the boundary layer. He reportedly sought somewhat unsuccessfully to
measureinertialcurrentsduringhisotherwiselongandproductivecareer.Nowthese
circular currents are known to be ubiquitous in the ocean, and indeed often appear
ascycloidalloopsin icedrifttrajectories(Section2.5).
Ekman realized that ideally the integrated mass transport in the rotating bound-
arylayerwouldbeatrightangletotheappliedstress.Thismeans,forexample,that
a southerly wind along a west coast in the northern hemisphere would drive sur-
face water onshore,which would in time set up an onshore sea-surface tilt (coastal
setup),drivingageostrophicallyadjustedcurrentin thesamedirectionasthe wind.
This current would in turn produce a bottom boundary layer, with offshore mass
transport.Asteady statecouldbeachievedwhenthe onshorewinddriventransport
atthesurfacebalancedtheoffshoretransportinthebottomboundarylayer.Withthe
opposite wind, bottom water would be driven onshore, balanced by offshoretrans-
portatthe surface.Thissimple conceptualmodelexplainsmuchabouthowcoastal
sea levelvariesin responseto wind, andwhy swimmingoffOregon(orCapetown)
beachesin summer,when thereis a persistentnortherly(southerly)wind,is notfor
thefaintofheart.
.
