Kyoto FDEPS lectures 4-7 xi 2007
Dynamics of oceans and atmospheres
P.B. Rhines
University of Washington

DAY 1• 1. rotating, stratified fluids: oceans and atmospheres– vorticity: a vector-tracer in classical homogeneous fluids• geostrophic adjustment, thermal wind• 2. wave dynamics: fundamentals, group velocity,
energetics, ray theory• potential vorticity (PV)– vortex stretching, Prandtl’ s ratio, geography of PV• 3. Rossby waves• 4. instability => geostrophic turbulence; subtropicalgyres: dynamics, jets and gyres• 5. meridional overturning circulations and thethermohaline circulation• 6. Teaching young undergraduates about the global
environment• 7. Seminar: subpolar climate dynamics observed fromabove and below: altimetry and Seagliders

Texture

Andy Goldsworthy

AGU, 2003

DAY 2

Kyoto FDEPS lectures 4-7 xi 2007
Dynamics of oceans and atmospheres
P.B. Rhines
University of Washington
DAY 2• 1. rotating, stratified fluids: oceans and atmospheres– vorticity: a vector-tracer in classical homogeneous fluids• geostrophic adjustment, thermal wind• 2. wave dynamics: fundamentals, group velocity,
energetics, ray theory• potential vorticity (PV)– vortex stretching, Prandtl’ s ratio, geography of PV• 3. Rossby waves• 4. instability => geostrophic turbulence; subtropicalgyres: dynamics, jets and gyres• 5. meridional overturning circulations and thethermohaline circulation• 6. Teaching young undergraduates about the global
environment• 7. Seminar: subpolar climate dynamics observed fromabove and below: altimetry and Seagliders

OSBwaves: more about steady radiation, group velocity:-2 dimensional waves from an oscillating wave source-waves generated with a mean flow (or without mean flow but with amoving wave source)-internal gravity waves, NH/U, Rossby waves: wave patterns and blocking

In very shallow water, undular bores occur with both gravity- andcapillary nature (backward and forward of the bore front,
respectively); here in a 5m channel.

Knight Inlet, BC
Undular bore anddownslope jet forced
by rapid tidal flow
over a bankDavid Farmer, IOS/URI

internal gravity waves: rays and modes
Jim Renwick, GFD lab Univ of Washington

Waves: modes and rays and wave/mean-flow interaction at the base of themixed layerinternal gravity waves driven by oscillating 2
dimensional cylinder. Viewed with shadowgraphNotice reflection at base of mixed layer
GFD Lab, Univ of Washington

frequency close to N..some generation of harmonics
and some turbulent mixinginternal gravity waves: a circular cylinder moves to theright steadily, horizontallynotice the fluid which is pushed ahead of the cylinder, with too
little kinetic energy to rise against the stratification. In areference frame moving with the ‘mountain’ this would beblocked fluid upstream of the mountain. It is transmitted bylong, low frequency gravity waves, visible in previous slidePV dynamics (PV = potential vorticity)uses the vorticity conservation (‘vector tracer’) property, but accounting forbuoyancy forces
PV conservation and flux (transport); Haynes & McIntyre JAS 1996
β-effect, spheregeostrophic adjustment in a cylinder with 2 –layer stratification.
A ball of fluid is injected at the interface and allowed to ‘slump’and spin. Shall we try this during the lecture?

Rossby waves

Rossby waves (barotropic mode) evolving in x andtime (left); dispersion relation (right)

Green function for Rossby waves driven by a compact
oscillating forcingbeta plumea steady, diffusive circulation gyre driven by a delta-function of stress curl; lop-sided,
extending far to the west of the forcing as in an ‘arrested’ Rossby wave

convection is simulated by diapycnal mass-flux; it drives an upper level
cyclone and deep anticyclone, deep and shallow western boundary currents
and a Stommel-Arons interior circulation; with continental-slope topography
a deep topographic gyre competes with the simple poleward interior flow.

The β-plume: Green function for steady, dissipative βplane vorticity equation, 1-layer fluid

Ocean gyresimulations
Hallberg &Rhines 2000

Subtropical gyre
dynamics, thermodyanamics andbiology

Palter, Lozier & Barber
Nature 2005

Williams,
Follows,
Migillicuddy
Nature 1998

Oschlies,
GarconNature1998Jetstreams, Storm-tracks and Subpolar Ocean gyresPeter Rhines
PO sem 2v07
in collaboration with Thomas Jung (ECMWF),
Sirpa Häkkinen (NASA Goddard Spaceflight Center),
Eric Lindahl and Alex Mendez (UW)

Jets, near and far

Science, 2007
special issueof JAS, 2007

Nature, 1994

G.P.Williams, JAS 1978 et seq.,
Yoden & Yamada JAS 93

Jets, shallow and deep:
Heimpel, Arnou & Wicht, Nature 2005

Multiple jets of the Antarctic Circumpolar
Current south of Australia
Sokolov & Rintoul 2007:
the three classic water-mass boundary
fronts are fragmented into
multiple filaments.

Sea-surface heightgradient, Southern
Ocean, with 3 different
choices of time-averagedflowChelton, Schlax, Freilich & Miliff Science 2004
4-year mean wind curl from QuikSCAT winds:persistent topographically related ocean frontal SST=>wind stress modification

Cold disk
Cold disk

high rotation

low rotation

Jets occur in rotating fluids for many reasons, here driven by thermal convection in a bowl-shaped basin. The jets inthe lefthand image occur due to the very strong topographic PV gradient, at high rotation (low Rossby number).
Condie & Rhines ‘Topographic Hadley Cells JFM 1994; Rhines ‘Jets’, CHAOS 1994.

Zonal channel with β-effect: turbulence makes jets

2-layer model,
Thompson & Young
JAS to appear 2007
Bottom friction isessential in limiting
amplitude ofcirculation and heat
flux
Local inhomogeneity
generated by
the spontaneous
formation of zonal jets
limits the traditional use
of turbulent diffusivities
to describe domainaveraged eddy fluxes.
βλ2/U=1/2 upper, 1 lower

U1, U2
zonal velocity
and meridional
PV structure,baroclinic instability
driven 2-layer
channel flow
. The upper layer
is more wavelike andzonal jets are more
effective barriers totransport at upper levels(Greenslade & Haynes2006). The lower layer,on the other hand, ismore turbulent andallows larger excursions
across the jet paths.

PV staircased(PV)/dy

PV vs. lat

βλ2/U=.5
κλ/U=.02

βλ2/U=.75
κλ/U=.08

Hoskins+Ambrizzi
JAS 9300

Branstator JClimate 02

•

JETS: elongated, intense, often persistent fluid flows. (from word ‘jut’ as jut out, Latin‘jactare’, to throw or cast) .

•TRADITIONAL dynamical view: formation through baroclinic instability of a broad, tilted wateror air-mass boundary, with frontogenesis at lower boundary or tropopause.

•

turbulent fluid view: stirring of potential vorticity (PV) leads to momentum flux that concentrates
jets and balances with far-distant countercurrents. Spontaneous jet formation in a channel with asource of energy (wind, baroclinic instability) (Taylor 1915, Dickinson 1969 JAS, Rhines 1977, Rhines &Holland 1979)•

downstream development view, Chang et al. (2004 J Clim), Hoskins & Simmons… baroclinic wavepackets•

wavy view: Rossby wave propagation occurs on surfaces with PV gradients…due to β,
topography, sloping isopycnal surfaces, velocity shear•

topographic view: strong mountainous topography is a PV anomaly that can focus broad zonal
flows into intense jets and give zonal structure to principal annular modes (e.g. Taguchi & Yoden 2002,
Rhines 2007 JAS)

Momentum transport by the waves sharpens jets, and barotropizes the mean flow. In
fact, the basis of baroclinic instability lies in counter-propagating Rossby waves, one
above the other, yet the basics of jet formation involve the reaction to PV stirring, which
is nonlinear, perhaps turbulent
FP Bretherton QJRMS 1966, Methven et al. QJRMS 2005,6, Rhines The Sea 1977, DAO 1979, Chaos 1994

•

Jetstream and storm track in the Atlantic:– concentration of meridional energy/moisture transport.
– leap-frog exchange of meridional energy/moisture transport with oceanic MOC– long distance communication via the jet stream waveguide– role of standing wave field: symbiosis of jets and eddies– PV stirring and water mass boundaries: jet makers– topographic jet generation•

Atlantic subpolar ocean gyre: driven by (and driving) the atmospheric storm track and
its Greenlandic focus– satellite altimeter view of surface circulation• where does the warm water flow north to reach the Nordic Seas and feed the
MOC?
• SSH : trend and eof structure showing deceleration and shrinkage of SP gyre
– yet connection with deep MOC outflow not known• EKE– surface drifter view
• Lagrangian and Eulerian circulation• Î hydrography, heat and fresh-water flux: the warm, saline invasion of theNordic Seas
• transport and transformation on the θ/S planeSouthern hemisphere and northern hemisphere circulations:(dynamic height at 1000 Hpa (colors: blue = low pressure cyclones, red=high pressure anticyclones), 300 Hpa, 30 Hpa 1993
(NH), 1996 (SH) winters, 100 days eachSouthern hemisphere and northern hemisphere circulations:(dynamic height at 1000 Hpa (colors: blue = low pressure cyclones, red=high pressure anticyclones), 300 Hpa, 30 Hpa 1993
(NH), 1996 (SH) winters, 100 days eachCyclogenesis west of Greenland, lee cyclogenesis east ofCape Farewell, strong penetration of storms into the Arctic

Hoskins & Hodges(MWR 2003)
storm tracks basedon vortictiy

track density

mean intensity

Annular modes withwavenumber-1
sinusoidal topography

Taguchi & Yoden
J Met Soc Jp 2002

kinematically, you can make a pair meandering jet by simply adding a zonal flow to a barotropic
eddy train,
U = Az + B cos(kx) cos(ly)AGU, 2003

zonal wind (m/sec) at 45W with Greenland topography
JFM 1993“Svairdrups”

In eddy and jet studies, the prominence of topography comes from the process ofbarotropization, the cascade of energy toward tall, nearly barotropic structures
which can be viewed as a consequence of the enstrophy cascade (the stretching of PV
contours) and/or of merger of like-signed baroclinic vortices. A key issue is whetherfragmentation of PV continues or is terminated during the cascade (hard-core vs. soft-anddeformable vortices).
Dissipation limited: a weak dissipation example where it plays out fully is Larichev & Held,
Held & Larichev (JAS 1996, JPO 1995) β-plane channel, yet Thompson and Young (JAS2007 in press) argue that surface dissipation is controlling, and must appear inparameterizatio
of meridional heat transport by jets
{This does not contradict the instablity of columnar vortices of scale much smaller thanthe deformation radius (Dritschel & Ambaum Phys. Fluids 1999)}

Barotropization of a two-layer zonal jet (Rhines,The Sea, 6, 1977)(as exemplified in EP flux analysis of ‘baroclinic life-cycles’ of the atmosphere); instability followed by eddy-eddy
interaction, geostrophic turbulence cascade (taller, wider), faster barotropic Rossby wave radiation.

upper
layer

time =>

lower
layer

Hakim, AS542 UW

Topographic flows: we now introduce the effects ofmountainous topography, which owing to the ‘vertical stiffness’ imparted by rotation, is greatly influential. On an f-plane, the Rossby number, U/fl,
topographic height and Froude number Nh/U are key parameters.

(i) 2D stratified flow over bump of height h (buoyancy freq N upstream flow U)
Nh/U (ii) 3D stratified flow …over or around
Nh/U crit ~ 2(Schaer+Durran, JAS 1997)
dispersive lee waves softens the ‘sharp’ hydraulic effects(iii) f-plane rotation, unstratified: Taylor column dynamics
flows ‘around’ if h/H > Ro (Ro = U/fL).
(iv) f-plane rotation weakens blocking (Nh/U crit =>3)Taylor column => Taylor cone Nh/U > 1 again! (independent of Ro)(v) β-plane flows-large-scale potential vorticity (PV) gradient-contours of constant background PV (f/h = const)
bend Equatorward over a ridge, locatinga cyclone over its crest for very slow flow
-dispersive lee waves, semi-circular wavecrests-hydraulic structure in some limits (planetary geostrophic)
where the waves are non-dispersive-strong upstream blocking (‘Lighthill mode’) for
βL2/U>1

Nh/U = 1, 2, 2.5, 3, 4, 6

pressure drag occurs when the anticyclone shifts
upstream as wake vorticity is shed, placing theEquatorward flow over the lee downslope

Impulse (the time-integrated force on the solid Earth)is summed up by meridional PV flux:<q’v’> which expresses the x-averaged force on
the Eulerian fluid along a latitude circle ~ (f/H)<h’v’>Petersen, Olaffson,
Kristjannson
JAS2003

Lee Rossby-waves in the wake of a cylindrical mountain (McCartney JFM 1976)

Rossby waves are ‘one-way’: their phasepropagation has a westward component
relative to the fluid: thus they exist as lee
waves for an eastward flow but not a
westward flow. Wave drag peaks at:
8.2 δ/ε times the ‘naive estimate’,ρfUL2δH
where δ=h/H is the fractional mountain height, ε the
Rossby number, U the mean flow, L the radius and H
the total fluid depthnote strong correlation of meridional velocity
and topographic height…..wave drag. Also notethe beginnings of jet formation southeast of themountain, even in the linear theory

wavenumber diagram for Rossby waves in steady zonal
westerly flow (U>0)

A westerly (prograde, cyclonic) zonal flow
encounters a small mountain(at 2 o’clock). Rossby wave dynamics
produces standing waves downwind, aconvoluted lee cyclone, intense jet structurewrapping round the mountain, and a ‘Lighthill
block’ upstream. This stagnant blocking
region is (in linear, yet finite topography,
theory, a Rossby wave with vanishing intrinsic
frequency and upstream groupvelocity for merid. wavenumbers < (β/U)1/2 .
Note the ruddy pressure features which
are fine-scale evaporative convection cells,
pillar-like cyclones. The edge of the blockis outlined by convective rolls.
Here the controlling parameter βa2/U > 1
meaning that the wake is stable; smaller valuesof this parameter yield unstable wake and transien
Rossby waves which ironically fill the hemisphere(they are not simple lee waves). See Polvani,Esler, Plumb JAS 1999 for a numerical study
with some of these features.

Streak image of the same experiment (dots 2 sec apart) showing intensity of jets near mountain, lee Rossby waves and upstream
blockpressure fieldand (stripes)
PV field

Planetary-geostrophic regime: exact solution by integration alongtime-dependent characteristics
Rhines, JPO 89

Eastward (westerly) flow over a mountain, barotropic single layer, spherical shallowwater model; Northern Hemisphere only. Note winding of PV into spiral above
topography, concentrating wake into jet. Cyclonic gyre in wake reaches north almost
to PoleShallow water on a sphere: T127 model: zonallyaveraged zonal flow and PV: (initially uniform superrotation). Here the blocking / wake instability parameter βa /U2

is 0.36-1.4 depending on whether a is chosen as radius or diameterU(latitude)
t=0

PV

initial zonal
velocity
final

upstream blocking,strong shear on
Equatorward flank

t=300
homogenized0

m sec -120

both hemispheres are filled with wave activity; after initial linear lee Rossby wave
generation, upwind blocking supresses Rossby-wave wake. There is a considerable
life cycle when, as here, the frictional damping is very weak.

migrating critical layer produces staircase PV field(mountain at 60N, easterly/westerly initial zonal flow with criticalmountainlayer for stationary waves)zonal veloc (zonal
average)PV

t=365dFinal
t=0
Initialzonal windhomogenizedhomogenized
pv discontinuity

0

20

40 m sec-1

note strengthening of both eastward and westward zonal flow…particularly the
westward low-latitude jet; the polar anticyclones are gone!

L

H

L
H

Moisture flux during high and low NAO: concentration in the high-latitude storm tracks of the ~ 2
petawatts of latent heat flux … whichis ~0.7 Sverdrup (0.7 megatonnes/sec) of freshwater flux
1993 JFM
1996 JFM

Mountain drag is associated with a strong northerly flow rounding the high groundanticyclonically, setting a lee cyclone at the beginning of the wake….as in a
downwind-displaced f/h contour.
This is the dominant flow round the Rocky Mts. but is not characteristic of theflow round Greenland.
Role of cold-air outbreaks….
Direct thermal forcing of the wintertime Arctic forces a high latitude easterly
flow and anticyclonic polar vortex at low levels; Rossby wave radiation from low
latitude does the same.
Cyclonic Arctic circulation comes thermal forcing and from invasive
cyclones: bodily poleward transport of PV.

Pressure drag on Greenland•

These flows generate waves and wakes, and in doing so exert forces on the topography, with virtuallyequal and opposite reaction forces on the atmosphere. Taken together, the pressure drag on all the
Earth’s topography, plus the frictional stress at the base of the turbulent boundary layer, exerts a zonal
force which changes the angular momentum of the solid Earth…the length of the day. About 90% of
this pressure drag comesfrom the atmosphere, the remainder from the ocean.
In this manner, our wrist-watches become virtual instruments to measureatmospheric angular momentum and the drag forces that alter it.

The length of the day varies seasonally by ~ 1 millesecond, largely due to the change in atmospheric angular momentum.

mountain pressure dragJan 2001

T159

T511

July 2001

Brown, QJRMS 2004

1989 JFMA:NAO index positive

Synoptic storm
tracks arebeneath stratosphericpolar vortex

Greenlandcolors: 1000 HPa near-surface dynamic height(blue=low pressure, red=high)contours:
jet stream level 300 HPa, stratosphere 30 HPa

1996

JFMA
(NAO index
very negative)

Storm tracks areusually southof stratosphericpolar vortex
Greenlandcolors: 1000 HPa
red contours: 300 HPa
black contours: 30 HPa

Greenland Tip Jet:
Doyle & Shapiro Tellus 1999; Pickart et al. Science 2003, Moore & Renfrew J Clim 2005

T95

T285

T799

Air Sea Heat flux
at various resolutions

Drag at various
resolutions (twocase studies,
20041226, 20050207)

Interesting cyclogenesis begins to appear in Baffin Bay at high resolution.
time sequence of SLP. This is prominent in the storm track spaghetti diagram in the next slide.

•In a series of numerical experiments at ECMWF, the flow in the Atlantic sector has been
examined as a function of model resolution.
(Jung & Rhines, JAS 2007 in press). Greenland’s 3km high topography generates strong
downslope-jet activity which spills out over the Greenland Sea; this is not resolved bytypical resolutions but begins to appear at about T255. Mesoscale model simulations (e.g.,of Bromwich, and Shapiro and colleagues) capture such features, but here they are present
in a global simulation.
Note the impact of resolution on the lee cyclone in the next images.

Jung & Rhines, JAS 2007 in press

250 HPa level case study for high drag (short integration)

T95

T255

T799

cases of cyclogenesis: resolution has a notable effect on an Eulerian measure of cyclogenesisWe explore the east-west component of pressure drag on Greenland.
pressure drag (red) and NAO idex
15-day smoothed

1980

2002

The 1000 HPa dynamic height fields that correspond to periods of high pressure drag on
Greenland are shown next, at lags of -4, -2 , 0,+2, +4 days. The pattern is quite local,
dominated by a low east of Greenland, with a lobe of high pressure farther to the southeast.
West of Greenland the pressure anomaly is surprisingly small. It suggests a relation with the
Atlantic storm track more than the deflection of a wind from the west, for in fact thewesterly zonal flows are peaking south of this latitude.

•The next figures are animations of the northern hemisphere circulation for a high-NAO(1989) and low NAO (1996) winter, respectively. They show many things, including strong
vertical interaction between clusters of cyclones and the stratospheric polar vortex. Synoptic
activity is felt in the stratosphere! A strong sudden warming is seen in 1989.

-6

-2

high frequency
variance composite
maps: 1000 HPa +2
level showing
storm track covariant
with pressure dragon Greeland-4-

0 days lag

+6

-6

-4

lag 0 days

-2
Z50
stratosphericpolar vortex level+2+4

number of cyclones in winter…observations (ERA-40) and various model resolutions T95 = 210 km grid; T799 = 25 km gridpotential
temperature
at tropopause
PV2 surface
and sea levelpressureDownslope winds increase wavedrag (by Bernoulli) here in a layer of CO2

Mel Shapiro’s Greenland flights

Ro = ∞
Nh/U = 1.5

Ro = 0.42
Nh/U = 1.5

Petersen, Olaffson,
Kristjannson
JAS2003

Schär (JAS 93): PV is transported along the intersections of the Bernoulli-function and isentropic surfaces in a statisticallysteady flow….

Schär & Durran
JAS 97
also: tip horiz
vorticity to makevertical vorticity
Rottuno et al. JAS
99

Ertel potential voticity generation by breaking lee gravity wavesL the PV generation as well as the gravity-wave momentum flux alter the geostrophic
circulation

Chen, Hakim & Durran, JAS 2007 subm

t=20hPV and zonal flow
generation in flow
over a 1.5 km
high mountain(dipole of PV,
decelerated wake)Chen, Hakim & Durran,JAS 2007 in press

t=30h

t=40h

t=50h

Orographic gravity waves over Greenland observed:
Limpasuvan et al. JGR 2007

Overturning circulations•

Oceanic overturning circulations: coexisting with ‘horizontal gyres of wind-forced circulation• MOCs have an easier time in the oceans than in theatmosphere:a ring of air moved 1000 km north gains westerly velocity
of 100 m sec-1 There is not enough energy available to utilize thismode: the Hadley cell is limited in north-south extent. Forces (eddymomentum flux from PV stirring) and non-symmetric circulation
are required to support extensive meridional excursion.

channels and conduits for heat- and fresh-watertransport

After Schmitz (1995)

Lateral penetration of convected water masses: Gradual diffusive closure of nearlybalanced circulations:(o) the linear heat-up problem(i) geostrophic adjusment followed by(ii) Elliassen-Sawyer overturning(iii)~ ‘slow diffusion’(iv) β-plumes

PV inversion: using a model of convective destruction of PV. The modelled
or diagnosed PV field is associated with a field of azimuthal circulation,
displaced mass, and interacts with the meridional overturning circulation
Marshall & Schott Revs Geophys 99

viscous overturning in a rotating cylider:
the radial/vertical plane transmits stress from the top plate (which is at restin the laboratory frame) and the bottom of the cylinder (which is rotating)

sugar
syrup

Overturning cells in an annulus of
fluid between concentric cylinders(the inner cyclinder is rotating, theouter cylinder is stationary(Taylor-Couette flow).
The cells transmit torque between
the solid cylinders more strongly
than would pure viscous diffusion.
(The same 2D equations govern
thermal convection, and theNusselt number expresses theanalogous increase in heat flux
above the diffusive rate).

Sink-driven flow in a rotating, stratified fluid: the cyclonic spin of the fluid
would be resisted by bottom Ekman friction (and all radial inflow
concentrated there in this tornado vortex); However, stable stratification
resists and forces continuing MOC within the fluid. The azimuthal velocity
and shear is so great that it tears up the stratification (originally 2 layers)

GFD lab, Univ of Washington

Dense plume flowing down a sloping valley in a rotating fluid(model of dense downslope flows in the Weddell Sea)
Elin Darelius, Univ of Washington GFD lab
particle paths are helical,
with Ekman driven meridional
overturning transmitting theboundary stress into thefluid. (Looking up the sloping
valley)Lumpkin & Speer’s JPO 03 discussion of the Atlantic MOC, here plotted against potential
density and latitude. Even though we know there is much east-west structure (boundary
currents, horizontal gyres as in Reid’s maps) the zonally averaged MOC ‘looks like’ thesimple 2-dimensional box models, for example Winton’sSsea
surface

O2

Lumpkin & Speer JPO 2003

AAIW

NADW

The ACC is the only
ocean current with The
Problem (how to flow meridionally, given theabsolute angular momentum constraint)..yet it
has ample topographic
bottom slopes to lean on:
these clearly balance thezonal wind stress thatdrives this greatest of all
ocean currents
meridional circulation
implied by tracers in the
Antarctic
Circumpolar Current
MacCready & Rhines

Oceanic
meridional
overturning
strength vs.
meridional
baroclinic
dynamic
heightgradient in
HADCM3(Thorpe et al 2001)

A change in the MOC transport may be associated with some measurable change in the meridional
density gradient. HadCM3 finds a very close correlation between Atlantic overturning rate and the S-N
gradient of steric height from 30S - 60N through the W Atlantic. But, there is a possible oversensitivity ofmodels to subpolar buoyancy/Labrador Sea described next.

Spall, JPO 2004 Cooled Basin with shelf forced by inlet dense water plume:the ‘MOC’ of the basin is largely achieved with eddy mixing from the shelf-edge/

The connection between primary horizontal circulation and the meridional
overturning for a symmetric vortex or 2D circulation is expressed by the
Eliassen-Sawyer equation (see Hoskins & Draghicci, 1972)

As with the equations for Rayleigh-Benard convection, the overturning streamfunction
and horizontal vorticity is of interest. In an axi-symmetric or 2D ‘zonal channel’
simulation the connection between primary horizontal circulation and the meridional
overturning
for a symmetric vortex or 2D circulation is expressed by the Eliassen-Sawyer equation(see Hoskins & Draghicci, 1972)

Hoskins,Draghici &Davies QJRMS 78
Thomas, Tandon & Mahadavon, Revs Geophys to appear 2007

Green’s function for the E-S equation (see Thomas et al. op cit.)
This is one of a class of ‘slow diffusion’ equations in which a compact regionof convection or mixing propagates outward through an interactive
adjustment of the thermal balance and diffusion of angular momentum

3D frontal instability induced by wind leads to downwelling by bolus flux,
PV destruction
Thomas et al. 2007 Revs Geophys submittedAtmosphere-ocean coupling: heat, moisture fluxes, wind-stress
Meridional energy transport in the climate system
Is the ocean heat transport important to climate?

Lau’s JAS 1979 winter diabatic heating of the 700mb-1000mb lower atmosphere. Peak values are 100-150
watts/m2 in the subtropical storm track regions

Held et al. (J.Clim.02) 100mb-1000mb diabatic heating for JanuaryQnet, net atmosphere-ocean heat flux, watts/m2 (Keith Tellus 95)(annual average)

It should be noted that because the sun heats the ocean, O,
but does not cool the atmosphere, A, the most useful mapsof Qnet for A will differ those for O by the short-wave insolation.

(from Thompson+Wallace J Clim 2000)
30 year trend in advection of time-averaged
winter temperature (925-500 Hpa av.)..anomalous velocity and advection, cooling the ocean while warming the land in bothAtlantic and Pacific sectors. Could these oceanic advective heat sources be the root cause ofthis contribution to global warming over Eurasia?

U ∂T / ∂x

THE END

An evacuated glass vessel with water in it illustrates the Clausius-Clapyron relation
between vapor pressure of water and temperature. The water is pushed from the vessel in
my hand to the ‘cold ball’, and the vapor pressure difference between the two ends is close
to the hydrostatic pressure measured by the column’s vertical displacement. One can fillout the curve and see the greater sensitivity (to temperature) of water vapor production at
high, ‘tropical’ temperature. This all works because we shake the vessel so that a thin filmof water lies under my warm hand. It illustrates a key variable in the climate system.
When shaken this water ‘clinks’ like metal,vapor cavities opening up and slamming shut.

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FDEPS Lectures, November 2007
P.B. Rhines, Oceanography and Atmospheric Sciences, University of Washington
Rhines@ocean.washington.edu
www.ocean.washington.edu/research/gfd
These lectures will address the dynamics of oceans and atmospheres, as seen through theory, laboratory
simulation and field observation. We will look particularly at high latitudes and climate dynamics of the ocean circulation
coupled to the atmospheric storm tracks. We will emphasize the dynamics that is difficult to represent in numericalcirculation models. We will discuss properties of oceans and atmospheres that are both fundamental, unsolved questionsof physics, and are also important, unsolved problems of global environmental change.
Lecture 1:
Is the ocean circulation important to global climate ? Does dense water drive the global conveyor circulation?
Fundamental questions about oceans and atmospheres that are currently under debate.
The field theory for buoyancy and potential vorticity.
Basic propagators: Rossby waves and geostrophic adjustment.
Potential vorticity: inversion and flux.
Lecture 2:
How do waves and eddies shape the general circulation, gyres and jet streams?
Almost invisible overturning circulations.
Lessons from Jupiter and Saturn.
The peculiar role of mountains, seamounts and continental-slope topography.
Lecture 3:
Dynamics of ocean gyres and their relation with the global conveyor circulation.
Water-mass transport, transformation and air-sea exchange of heat and fresh water.
Ocean overflows and their mixing.
Decadal trends in the global ocean circulation.
Lecture 4:
Heat, fresh-water, ice: convection in oceans and atmospheres and the texture of geophysical fluids.
Lecture 5:
Teaching young students about the global environment using the GFD laboratory: science meets energy andenvironment in the lives of Arctic natives
Seminar:
Exploring high-latitude ocean climate with Seagliders and satellites

Kelvin waves, inertial waves in shallow rotating fluidgeostrophic adjustment: scenes from the North Pacificsubtropical front region: Gregg, Brainerd, Hosegood, Alford