Kyoto FDEPS lectures 4-7 xi 2007
Dynamics of oceans and atmospheres
P.B. Rhines
University of Washington• 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. Seminar: subpolar climate dynamics observed fromabove and below: altimetry and Seagliders

Texture

Andy Goldsworthy

AGU, 2003

water evaporates
from the Great
Lakes when cold
north winds blow
over them. It
soon condenses
back into water,
as cloud droplets
which then rainor snow
out…The lakewater hasbecome cloud,and then thecloud piles up as
deep snow,
downwind of thelakes. This iscalled ‘lake-effectsnow’.

Erika Dan temperature section, 600N
Labrador-Greenland-Rockall-IrelandWorthington+Wright, 1970

warm, saline water moving
north from the subtropics

shallow continental shelf circulation (unresolved in CCMs)
deep overflows from Denmark Strait/I.S. Ridge

deep winter mixing, sensitive
to upper ocean low-salinity
watersFive Davis Strait Seaglider temperature sections showing Arctic
cold water entering the Labrador Sea, have unprecedented spatialresolution
Eriksen & Rhines UW

boundarymixing/upwelling

entrainment

broad upwelling, yet much of it recirculates below the mixed layer

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

Cold disk
Cold disk

high rotation

low rotation

spatially homogeneous, density stratified rotating convection viewed from the side:
note streaks show w ~ u in small plumes yet also mesoscale structure is present

mixed layer base

GFD lab Univ of Washington

potential vorticityand buoyancy are
the fundamental
field variables forcirculation(here in 4box-ocean
wind-drivensimulations)Hallberg & Rhines Dev. in Geophysical Turbulence, R. Kerr Ed., 2000

Theta-S diagram for Atlantic ocean (Southern Ocean
to subpolar North Atlantic)

cylinder wake in a soap film

Marvin Rutger

textures of different dynamical variables

Vorticity in a ‘classic’ non-rotating fluid

Vortex lines move with the (ideal) fluid….A famous billboard in Times Square,
New York, 1950s. Note the size of the vortex rings, which are real.

vortex lines are ‘vector tracers’ that move with thefluid

vorticity: teaching tornados‘Levitated’ balls with strong
vertical and horizontal shear
layers contain radial/verticalviscous overturning

Tornado vortex-2

Vorticity and forces:
I = ½∫ω x r dVor one-half the dipole moment of the vorticity field is equal to the ‘impulse’, or timeintegrated force exerted on a fluid…2/3 of which appears as momentum change of thefluid in 3D (the actual number depends uncomfortably on the shape of the control
volume, as it recedes to infinity).
(in 2D the expression for impulse, ‘½’ is absent, yet the momentum change in a 2D
fluid is still ½ I, that is ½ ∫ω x r dV) r=position vector, ω=vorticity vector Saffman,
Vortex Dynamics, CUP

the rest of the impulse
exerts a pressure force
on the fluid at a great
distance; this confusion
is resolved if the fluid
is slightly compressible
in which case all theimpulse appears asmomentum.

dipole wakes in thewake of the
Aleutian Islands
express the force
exerted on themountain slopes

Planetary Rotation:
gives stiffness to the fluid, creates ‘tall’ flow structures
In our discussion of vortex line tipping and stretching we can
now replace vorticity ω by absolute vorticity ω + 2Ω:
the planetary vorticity amplifier

Rotating fluids are filled with‘tall’ structures

Andy Jackson, WUN 2004

Influence of rotation I:
The Earth’s inner solid core is visible in the magnetic field; note thetwo maxima of the normal non-dipole field

After Gubbins & Bloxham (1985)

Morphology of magnetic field lines
from numerical dynamo simulation(Glatzmaier & Roberts, 1995)

Jets on Jupiter: a good place to think about tall structures vs.thin, gravitationally stablelayered Earth atmosphere. Here a deep, non-hydrostatic numerical model allows
structures to line up with the rotation axis.

(Heimpel, Aurnou & Wicht, Nature 10 Nov 2005)

planetary rotation canorganize the chaotictextures of turbulent flow
into coherent structures
GFD lab Univ of Washington

Maximenko et al2005

The geopotential: potential function Φ for gravity andcentrifugal rotation effects

the geoid Φ: for a symmetric model of Earth’s gravity

The presence of planetary vorticity amplifies effects ofline-stretching:a ring of air moved 1000 km north gains westerly velocity
of about 100 m sec-1 (for f=10-4sec-1) There is not enough energy
available to utilize this mode: the Hadley cell is limited in north-south
extent.
Forces (eddy momentum flux from PV stirring) and non-symmetriccirculation are required to support extensive meridional excursion.

A 2mm glass cylinder is held vertically…at restin the non-rotating frame…in a rotating
fluid…
Its 3D turbulent wake generates cyclonic tallvortices(Cormac Flynn, GFD Lab, Univ. of Washington also see
computer sims of Smith & Waleffe Phys Fl 99
Morize,Moisy & Ribaud, PhysFl 05)

cylinder removed, showing final barotropiccyclones
Turbulent flows exhibit remarkable transformation between
non-geostrophic and quasi-geostrophic flow, in both
directions. Here, a 3D turbulent cylinder wake converts intoa 2D field of cyclonic vortices. This is as if you inserted
your finger in the fluid as it rotates rapidly.

the surface of a rotating fluid, slightly moving ( Rossbynumber << 1)Dynamic height along latitude 60N from surface to stratosphere(1000 HPa to 30 HPa) for days 1-100 in 1996

30 HPa1000 HPalongitude 01800

Ocean currents at 50W longitude southeast of the Gulf
Stream, over 7 months, showing very similar structure
throughout water column: a strong barotropic modeeach line is ahorizontal current
vector plotted witheastward flow
pointing upwardrotational stiffness is related to inertial waves (often wave
motions express restoring forces that strongly effect steadycirculations too).

inertial oscillations viewed by the movement of thewater surface (essentially a pressure field).

geostrophic balance: the sea surface at the Gulf
Stream Tom Rossby, Oleander project, adcp based

geostrophic balance: the pressure field along north-south lines
in the atmosphere; day 1 1996 and day 180 1996
blue: 500 HPa dynamic height
red: sea-level pressure NCEP reanalysis datasteady, non-dissipative flows have a powerful Bernoulli function
conservation principle: both the pressure variation along a
streamline and across streamlines is known from the velocityfield.
• example: 2-dimensional flow around a circular cylinder.
Adding rotation simply adds a pressure field that is afunction of ψ. This shows how geostrophic flow haspressure gradient nearly perpendicular to the velocity, yetalways with important pressure variations along streamlines

2D flowaround acircular cylinder

Fig. The flow field (ψ) is at upper right. The pressure field for
different values of the Rossby number, Ro = ∞, 3.3 and 1.1

•

The pressure field for flowround a cylinder in a single-layer
rotating fluid, at moderate
Rossby number is simply thepressure for a non-rotating flowplus a function of ψbuoyancy: it’s tricky

Geostrophic adjustment: initial value problem that
ends up as a geostrophic flow

geostrophic adjustment: scenes from the North Pacificsubtropical front region: Gregg, Brainerd, Hosegood, AlfordVelocity spirals: thermal wind balanceone year current records at 2000, 3000, 3800m depth
in the deep western boundary current

Stommel’s coolingspiral at OWS Juliette(52.5N, 20W) is a
symptom of upward
Qnet

Plot of (u,v) velocity
components with depth
as a parameter fromhydrographic dataStommel, PNAS 1979

rotating and stratified flows..over simple mountains

Waves

Digital cameras readily do time-exposure streak images of particle paths(Nikon Coolpix 950)

group velocity theory: stationary phase integral

Moiré patterns and group velocityOSB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The table rotation rate is oscillated about its mean value toexcite waves, with a small mountain. Fast, long hydrostatic
Kelvin waves ans short non-hydrostatic inertial waves. 1 m
diameter cylinder, GFD Lab Univ of Washington

Kelvin waves, inertial waves in shallow rotating fluid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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 (barotropic mode) evolving in x andtime (left); dispersion relation (right)

Rossby wave Green function for an oscillating vorticity
source at the origin: with free-surface divergencebarotropic Rossby waves excited by uniform westerly (eastward)
zonal flow past a cylindrical mountain (McCartney JFM 1975)Subtropical gyre
dynamics, thermodyanamics andbiology

Palter, Lozier & Barber
Nature 2005

Williams,Follows,
Migillicuddy
Nature 1998

Oschlies,Garcon
Nature1998

TABLE OF CONTENTS••••••

Polar amplification of the two 20th C warming events
Storms and weather….ocean to stratosphere: continuity of theAtlantic storm track/Icelandic Low from subtropics to highArctic
Atmospheric and oceanic transports, strongly coupled, supply continental and polar
warmth, fresh water
The oceanic heat source: northward heat transport essential to wintertime driving of 3
scales of atmospheric circulation,
Transports by ocean circulation: connecting the Arctic and Atlantic– Erika Dan, 600N winter in the N Atlantic: deep, shallow andshelf water masses– Atlantic – Arctic exchange: Θ-S-transport (~heat,fresh-water transport) diagrams– Rapid and slow modes of response of Atlantic overturning:
Labrador Sea vs. Nordic Sea overflows– What matters to the global overturning circulation:• The freshwater cap and its movement: liquid and solid• Layering of deep-ocean water masses, and its
representation in models• Shallow continental shelves and communication withthe deep ocean

Arrays and instruments: establishing the baseline and sustaining
it in timeGlobal surface temperature has seen two major warmings in the20th Century: in the 1920s-30s, when it was very
concentrated around Greenland, and since the 1980s, when it
is much more global, yet still concentrated in high northernlatitudes.
Cod and herring fisheries responded to the much warmer
ocean temperatures, which lasted for more than 25 years.
Ironically we anticipate the ocean circulation slowing during
the current warming, whereas it is possible that anaccelerated oceanic meridional overturning circulation was afactor in driving the 1920s warming.

Surface Air Temperature

Delworth+Knutson, Nature 1999

Uppernavik, West Greenland SAT anomaly (Imke Durre)

The standing-wave structure with wintertime Icelandic andAleutian Lows gives the atmosphere some of the east-west
structure and gyre circulation familiar to the ocean. The
rapid radiative cooling in fall sets up a cold dome whichslumps under gravity, tending to create a surface polar
vortex which is anticyclonic, the convergence overhead
strengthening the polar cylonic vortex…yet mountains andvertical momentum transport can intervene, opposing thesurface high.

In particular, the Atlantic storm-track forms a continuous
connection between subtropics and the high Arctic.

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

Hudson Strait salinity at 50m August 1965 (J.Lazier)This is part of the only 3-dimensional hydrographic survey ever made of the Labrador/Irminger seas.

Cuny et al. 2003

Southward
moving lowsalinity waterfrom Baffin Bay

Northward
moving
Greenland
shelf water
Irminger
Current water
circumnavigating
the Labrador Sea

The solution? Instrument the Arctic Rim. Do ASOF.
Deploy the Eriksen Seaglider: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 closeto 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 athigh, ‘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.

Ocean advection, Arctic-Atlantic Connections, ClimateP.B.Rhines, University of Washington
Sirpa Hakkinen, NASA Goddard SPC
with David Bailey, Wei Cheng, Jerome Cuny, Trisha Sawatzky
WUN Climate teleseminar, 26iii2003

North Atlantic Oceanic Heat Advection is
Important to the Wintertime Storm Track,
Eurasian climate and weather and Global
Climatewww.ocean.washington.edu/research/gfd/gfd.html

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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