Ekman transport, pumping & gyres

Fric6onal effects: Ekman layer

• NeartheEarth’ssurfacethegeostrophicbalancebreaksdownbecauseoffric8on,eveninthelimitofsmallRossbynumber:

•  ThelayeroverwhichthisoccursiscalledtheEkmanlayer,whosethicknesshEkisontheorderof

2

21zu

xPfv

∂

∂+

∂

∂−≈− υρ

fhEk

υ≅

Thisisabout50mfortheoceananda500-1000mfortheatmosphere

Ekman layer in ac6on: tea leaves in a cup•  Setincircularmo8onwaterinacupwithtealeaves.Letitspindownandwatchthetealeavesaccumulateinthecenter

•  “Restframe”interpreta8on:inwardradialpressuregradientisapproximatelybalancedbycentripetalaccelera8on(V^2/r).NeartheboPomthecentripetalaccelera8onisweaker(whilehorizontalpressuregradientisunchanged)sothereisanimbalanceandinwardflow

Ekman layer in ac6on: tea leaves in a cup

•  Setincircularmo8onwaterinacupwithtealeaves.Letitspindownandwatchthetealeavesaccumulateinthecenter

•  “Rota'ngframe”(takeitan8-clockwise,asseenfromthelab)interpreta8on:theflowneartheboPomisclockwiseandaCoriolisforceactsonittowardsthecenter(thisforceislargerthantheadvec8onofangularmomentuminthelimitRo

Ekman layer in the atmosphere (near the Earth’s surface)

•  Flowisinwardinlowpressuresystems(cyclones)àupwardmo8on

•  Flowisoutwardinhighpressuresystems(an8cyclones)àdownwardmo8on

• NBUsefulresult:theinward/outwardmassfluxintegratedoverthedepthoftheEkmanlayerisatarightangletothesurfacefric8onforce(=“Ekmantransport”)

Surfaceweathercharton10/02/2008withsurfaceflow(arrowswithquiverevery5m/s)andsurfacepressure(ci=4hPa).FromTandon&Marshall(2008)

Coupling of oceanic & atmospheric Ekman layers

• Overtheoceanthesamefric8onalforceissharedbytheatmosphereandtheoceanattheseasurface

•  Thisdrivesthesameamountofmasstransportintheoutward/inwardcircula8on:theEkmantransportareequalinmagnitudebutoppositeindirec8on

FromGill(1982,Chapter9)

(inN/m2)

Ekman layers and Hadley, Ferrell, polar cells

ThesurfacebranchesofthecellsareEkmanlayers

Convergence/divergence of Ekman transport• …leadstoregionsofdownwellingandupwelling

•  Theassociatedver8calmo8onisontheorderof~30m/yr

WesterlywindTradewindsPolareasterlies

The“bowlshape”ofthethermoclineisaconsequenceoftheconvergenceofEkmancurrents

Ocean gyres (as seen at the sea surface)Annualmeandynamictopography(1993-2002)fromMaximenkoetal.(2009)–CI=10cm

Ver6cally averaged circula6on (in Sv) from ocean floats & hydrography

•  jkj

DeVerdiereandOllitraut(2016)

NB1Sv=10^9kg/s

Ocean eddies

Oceans and atmosphere in real 6me…

hPps://earth.nullschool.net

In-situ observa6ons are dominated by a “meso-scale”

Surfacetemperaturefrominfraredmeasurement

KEspectra(surface)

In – situ velocity measurements

Loca8onof“long”(~2yr)currentmeters

Depth

Amplitudeof8mevariability

FromWunsch(1997,1999)NB:Energyatperiod<1daywasremoved

1yrNB:Samevelocityvectorsbutrotated

MooringsintheNorthAtlan8cinterior(28N,70W)

Schmitz(1989)

Role of “ocean eddies”

•  Upwardtransportofheat(warmfluidgoesup,coldfluidgoesdown)

•  Thismaintainssharptemperaturevaria8onsinthever8caldirec8on(warmatupperlevels,coldatdeeperlevels)

•  S8rtracers(physical,chemical,biological)throughouttheocean

•  Keyroleinoceanheatuptake

“Thermohaline circula6on”

WorldOceanAtlasSalinity(0-500m)

psu

The “great oceanic conveyor belt”

Matsumoto,JGR2007

SpeerandLumpkin(2006)