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