Post on 23-Oct-2020
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)