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Rotating Fluid -Part II
A “GFD view” of the Ocean and the Atmosphere
(a follow up Raymond’s Lectures)
Arnaud Czaja
Source / sink flows –see Raymond’s lectures
“Basin”
“Channel”
Source / sink flows –see Raymond’s lectures
“Basin”
“Channel”No distinction betweenOcean & Atmosphere…
Central idea
• Constraint 1: Ocean & Atmosphere are rapidly rotating fluids: geostrophy is the leading order dynamics.
• Constraint 2: The two fluids must transport energy poleward (cold parcels move equatorward and warm parcels poleward)
Central idea
• This brings a key distinction between basins (~ocean) and channel (~atmosphere)’s geometry:
Basins: walls provide dP/dx and a large scale (eddy free) geostrophic heat transport is possible.
Channels: no zonally integrated dP/dx and the heat transport must involve eddies and / or ageostrophic effects (e.g., Hadley cell).
x
Pfv
o
1
Outline
• The energy constraint
• Basin dynamics
• Channel dynamics
The energy constraint
The energy constraint
Geometry: more energyimpinging at low than high
latitudes
Stone, 1978.
Assume infra-red radiation and albedois uniform
Observations
ASR IR
The energy constraint
The energy constraint
Poleward motionin ocean & atmosphere
Basin: Northern Oceans, Atmosphere
• Background
• Geostrophic mass transport calculation
• Heat transport
• Complications…
A classic:
oxygen distribution at 2500m
(from Wüst, 1935).
A classic:
oxygen distribution at 2500m
(from Wüst, 1935).
-Spreading from high latitude North Atlantic source region
-Large spatial scale of `tongue’ consideringthe narrowness of ocean currents
More recent sectionalong the `great tongue’
The “great oceanic conveyor belt”
The “great oceanic conveyor belt”
Broecker, 2005NB: 1 Amazon River ≈ 0.2 Million m3/s
Sv2010max
Atlantic ocean’s meridional overturning streamfunction
NB: From an OGCMconstrained by data(Wunsch, 2000)
136101 smSv
Can we measure the ocean circulation in basins using the
Geostrophic calculation?
• All you need is the thermal wind:
x
g
z
vf
o
Coriolis parameter
North-South velocityGradient with height
East-westdensity gradient
Global “inverse” ocean circulatioin and heat transport
Ganachaud and Wunsch, 2003
RAPID – WATCH array at 26N
RAPID array calculation
RAPID array calculation
Blackboard calculations…
Heat Transport
26N
Warm water
Cold water
East
North
Up opopoo McdxdzvcH
Heat Transport
26N
Warm water
Cold water
East
North
Up opopoo McdxdzvcH
Mo ≈ 20 Sv & Δθ≈10Kyields Ho≈1PW as required
Are there basins in the atmosphere?
Z
Density profileH~7km
OCEAN ATMOSPHEREX
Trade wind inversion
Different situation in the Tropics
2-3km
… “isolated” low level layer
Orography
Northward flow across the equator
East-African Highlands & the Indian Monsoon
Low level winds climatology (June-August)
ERA40 Atlas
Channel: Atmosphere, Southern Ocean
• Hadley cell
• Oceanic & atmospheric eddies
How to satisfy the energy constraintIn a geometry in which <dP/dx> = 0?
Zonally averaged atmospheric circulation (annual mean)
~100Sv
NB: Ocean: ~10-20Sv
Zonally symmetric
motions are the key energy
carriers in the Tropics
Total
Transient eddies
Stationnary eddies
Axisymmetricmotions
Zonally averaged atmospheric circulation (annual mean)
Frictionaleffects dominate
Ω
Eq
df/dy max at equator
Zonally averaged atmospheric circulation (annual mean)
Inertialeffects dominate
Critical (moist)temperaturedistributions leading to the onset of Hadley cell
Emanuel (1995)
Poleward heat transport in Hadley cell –see Q3
High gz
Low gz
Eumetsat/MetOffice infrared picture (daily composite)
Eddy motions are
the key energy
carriers in midlatitudes
Total
Transient eddies
Stationnary eddies
Axisymmetricmotions
Ocean eddies: the Movie
Ocean eddy heat transport from a ¼ º ocean GCM
From Jayne & Marotzke (2002)
Eddyheat transport
Total heat transport
“Shallow” Ocean (heat trspt ≠0)
“Deep” Ocean (heat trspt=0)
P
T
VLongitude
Height