*-- to quote the late Hermann Bondi, an `opportunity to
allow the bees in one's bonnet to buzz even more noisily than
usual.' *

**STOP PRESS:**
Stephen Thomson and I have now revised
our new paper submitted last year to
*J. Atmos. Sci.*, entitled
*Jupiter's unearthly jets: a new turbulent model exhibiting
statistical steadiness without large-scale dissipation*.
Here is
the revised preprint and an associated movie,
presented along with the famous Cassini polar-view movie that motivated
our work.

What has the above animation to do with communication skills, and with the
**public understanding of science**?
To find out,
click here **(new e-book under construction)**.
Those in a hurry may prefer
**lucidity principles in brief** (17K).
Some related musical fragments are
here. (Re
David Crighton CDs --
hardly any left now!).
Here's a reprint of my
Kobe Lecture
*Lucidity, science, and the arts:
what we can learn from the way perception works* (900K),
and a brief commentary on the implications for scientific foresight,
published in October 2006 as a *Focus* article in
*BlueSci*, Issue 7.
Also available are
electronic versions of the original published papers,
*Lucidity and Science Parts I, II and III*.
I
gave a
related talk, with musical illustrations,
at the 2013
Hay-on-Wye Philosophy and Music Festival
of the Institute of Art and Ideas.

Related to all this is a point raised in
the last of Professor V. S. Ramachandran's
wonderful Reith Lectures in 2003. On hearing the lectures,
I was moved to post here an
`Einsteinian
footnote'
to what was said in the lecture about the ancient problems of `self',
`consciousness', and `free will', and the possibility of a
solution `staring at us all along'...
Basic to it all, though often overlooked,
is *combinatorial largeness*. This
includes the unimaginably large
number of ways for complex systems to go wrong, a point
familiar to computer programmers.

The Earth system is a very complex system indeed but there are
some simple, hard facts about it that need wider recognition today.
And we scientists haven't pointed them out clearly enough until
recently. These facts concern the gas
carbon dioxide (CO_{2}) and its role in climate,
very different from the role played by water vapour.
My latest attempt to get the issues clearly, simply and quickly stated
is in the Postlude to a new
e-book under construction.

I've moved my older discussions of those matters to two separate pages.
The first is
a little factsheet on CO_{2}
-- a few facts about CO_{2}
that attract no serious controversy.
The second touches on
some of the wider implications,
trying to bring out the distinction between
the climate-system amplifier's *input variables* or `control knobs'
(such as anthropogenic CO_{2}) and
its internal or feedback variables
(such as water vapour, and naturally-fluctuating CO_{2}).
The discussion emphasizes what we know from studies of past climate,
independently of the imperfections of the big climate models.

*Note added December 2013:* I just came across a recent book
with well-documented insights into why there's been so
much confusion about CO_{2} and climate:
*Merchants of Doubt: How a Handful of Scientists Obscured the
Truth on Issues from Tobacco Smoke to Global Warming*,
by Naomi Oreskes and Erik M. Conway, Bloomsbury, 2010.

Understanding the Sun is important too.
Here's the latest on the solar tachocline.
WHAT A ROLLER-COASTER RIDE!
See
the third and fourth paragraphs below the colour cartoon,
now including a
set of exact solutions that
Toby Wood and I discovered in 2007,
modelling the
confinement of the Sun's interior magnetic field
and involving a nontrivial
interplay between magnetic diffusion and the
Lorentz and Coriolis forces.
This has now been thoroughly investigated and is the subject of a
major paper
in the
*Journal of Fluid Mechanics*
,
entitled
Polar confinement of the Sun's interior magnetic field by
laminar magnetostrophic flow
(1.1 Mbyte, © 2011 Cambridge University Press,
*J. Fluid Mech.* **677**, 445-482).
Here's a reprint of the
1991 `downward control' paper,
(2.1 Mbyte, © 1991 American Meteorological Society,
* J. Atmos. Sci.* **48**, 651-678)
demonstrating the gyroscopically-pumped
`Haynes-Spiegel-Zahn burrowing' that's so crucial to our
arguments.

Here's a first paper on turbulent mixing in the oceans,
entitled
*
On spontaneous imbalance and ocean
turbulence: generalizations of the
Paparella-Young epsilon theorem
*
(.pdf, 0.125 Mbyte, © 2010 Springer-Verlag).
The generalized epsilon theorems constrain turbulent dissipation rates
ε
in model oceans with realistic, nonlinear equations of state.
Together with empirical mixing-efficiency formulae the
theorems
bear on the `ocean conveyor belt' idea and why it's misleading
for some purposes.
This is a conference paper published in

Here's a brief essay
`On
thinking probabilistically' (pdf, 0.2 Mbyte).,
based on the beautiful
theorems of Richard Threlkeld Cox.
It is a reprint from the 2007 proceedings of
the 15th 'Aha Huliko'a Workshop on *Extreme Events*
held at the University of Hawaii in January 2007.
It tries to address some of the most deep-seated difficulties
in understanding
probability and statistics and, by implication, in understanding
science itself.
Even more than usual, the difficulties stem from unconscious assumptions.
I try to show how all this is related to natural selection and
why there's far more to it than
the outdated `frequentist versus Bayesian' polemics.

Frequentist thought-experiments are very useful
in some circumstances -- an important working tool.
But there is, I believe, a serious problem with
the old `hardcore frequentism' and its
influence on the teaching of undergraduates.
The trouble begins with the tacit
portrayal of probabilities as absolutes
-- as *the* probability of this or that
(i.e., with conditioning statements suppressed).
I believe this teaching practice to be deeply confusing,
and sometimes very dangerous,
as with the notorious cases of unsafe murder convictions via the
prosecutor's fallacy and even simpler statistical fallacies
(as in the
Sally
Clark case,
*the* probability that she didn't kill her babies,
etc). But the deepest and most dangerous confusion of all
comes from the hardcore frequentist or absolutist
view of probability values *as properties of things in the
outside world*, or material world --
i.e., as properties of
what science calls objective *reality*.

The `walking lights' display at the top of this page reminds us of
how we perceive reality, namely by unconsciously
fitting internal mental models to data.
Data consist of information arriving
from the outside world, such as patterns of light on
the retinas of our eyes.
Science works in fundamentally the same way,
though more slowly and more consciously and with more and better data.
So a coherent account of what science is requires us
not only to assume that reality exists but also,
crucially, to maintain a clear distinction between reality,
on the one hand, and models of it on the other. Models --
theories if you will -- are
partial and approximate representations of reality, some models
being better than others.
Probability theory is one of the most powerful tools at our disposal
for building good models of reality.
Indeed, it's arguably an *indispensable* tool for that purpose
(e.g., p. 158 and footnote 5 of the
essay;
see also the
literature on countless scientific topics including
quantum theory, statistical mechanics, noisy dynamical systems,
`stochastic parametrization' and stochastic modelling in general).
So, in any coherent account of what science is and how it works,
probability values and probability distribution functions
need to be regarded as model properties,
alongside all the other mathematical constructs we use in model-building.

So to insist that probabilities are, on the contrary, properties of things in the real material world is to preclude a clear understanding of what science is. We cannot distinguish between models and reality if the distinction is hopelessly blurred at the outset. And such confusion is incalculably dangerous. That's no exaggeration in a world whose fate depends on a clear understanding of science, and on the wise use of science. Here's a conference talk that pursues these points a bit further (pdf, 1.2 Mbyte), first given on 26 September 2007. (Of course there's no original thought here -- the clarifying ideas go back to Plato, Kant, Laplace and R. T. Cox and have been well vindicated by experimental psychology in recent decades, including systematic and detailed studies of the walking-lights phenomenon.)

The wise use of science in the UK, indeed the survival of good science, is

Participation in the 2006
Chapman Conference
on Jets and Annular Structures in Geophysical Fluids
prompted me to make available
a scan of my 1970 paper bearing on the anti-frictional
**self-sharpening of jets**
(*J. Fluid Mech.* **40**, 273-306)
*On the non-separable baroclinic parallel flow instability problem*,
as two .pdf (acrobat) files
(ca. 1 Mbyte each, © 1970 Cambridge University Press).
Here's
the first .pdf file, pp. 273-290,
and here's
the second, pp. 291-306.
Similarly, here's a scan of my 1982 paper to
*J. Meteorol. Soc. Japan*, **60**, 37-65,
*How well do we understand the dynamics of stratospheric warmings?*,
in which the **fully nonlinear
jet-sharpening problem** is discussed on page 47.
The key idea, that jet self-sharpening results simply from
potential-vorticity mixing at the side of the jet, is summarized in
Figure 5 on that page.
This may be the first appearance of the idea
in print; and the idea seems to be of generic importance for
understanding strong jets, such as the Gulf Stream and the great
atmospheric jetstreams, though less so for the weaker jets
often found in "beta-turbulence" experiments.
Again the full paper comes as
two .pdf files:
here's
the first .pdf file, pp. 37-50 (1.3Mbyte),
and here's
the second, pp. 51-65 (1.5Mbyte).
For a broader view of jets in general see below
(Marshall Rosenbluth Lecture and a recent AGU talk).

Regarding
potential vorticity (PV) as such, a review I wrote in 1993,
*Isentropic distributions of potential vorticity and their
relevance to tropical cyclone dynamics*,
is
available via this link
along with the
big 1985 PV-inversion review with Brian Hoskins and Andy Robertson
and other tutorial material.
The anti-frictional jet sharpening ideas are developed further,
after a historical survey, in a
review co-authored by David Dritschel and myself
that appeared in the
`Jets and Annular Structures' Special Collection
of the *Journal of the Atmospheric Sciences*,
**65**, 855-874 (2008),
*
Multiple jets as PV staircases:
the Phillips effect and the resilience of eddy-transport barriers
*
(.pdf, 1.5 Mbyte, © 2008 American Meteorological Society),
including an unconventional suggestion for
Jupiter (which, however, now seems superseded by
Stephen Thomson's work).
Here is an
earlier (1990) discussion of eddy-transport barriers.
Recent work by Richard Scott and David Dritschel
(2012,

Here's the
updated written version of my
Marshall Rosenbluth Lecture,
*The atmospheric wave-turbulence jigsaw*,
now
finalized
and in press (October 2013).
It gives yet another angle on jets, with a plasma-physics audience
in mind. Jets are important for
heat confinement in the fusion-power machines called
tokamaks and stellarators.
See also this little talk I gave at the
2011 Fall Meeting of the
American Geophysical Union,
*On jet dynamics and the DIMBO effect*:
compact pdf without movies
and
powerpoint version with movies. And
here is
the powerpoint
for the Haurwitz Lecture
to the American Meteorological Society
given in June 2013,
in which I try to pull some of this together and
set it in a wider context:
*A tale of two paradigms, with remarks on unconscious assumptions*.

Basic to much of this is the catalysis of potential-vorticity
mixing by a Rossby-wave radiation stress. The simplest
explicit example of such catalysis -- and its interplay with the
radiation stress itself -- is an old classic, the
Stewartson-Warn-Warn problem.
A short paper in
vol. **15** of
ADGEO
(*Advances in Geosciences*), 2008, pp.47-56,
gives a review of what's involved in such `catalysis'.
The title is
*
Potential-vorticity inversion and the wave-turbulence jigsaw: some
recent clarifications* (.pdf, 340 kbyte)
and the paper includes remarks on `Welander's goldfish'.

Jet self-sharpening, potential-vorticity mixing and
angular-momentum changes
are interrelated in a subtle way that
may appear paradoxical.
For instance, the natural jet self-sharpening process
causes the jet core to accelerate while reducing
the total angular momentum. How this works is
clarified in a
paper by Richard Wood and myself,
*
A general theorem on angular-momentum changes due
to potential
vorticity mixing and on potential-energy changes
due to buoyancy
mixing*,
(.pdf, 0.8 Mbyte, © 2010 American Meteorological Society),

For light relief, if you fancy it, here's my `geophysical' completion of Lewis Fry Richardson's famous turbulence ditty (like all these things, not completely accurate).

More importantly, here at last are the
hyperbalance equations
(final version),
a new and surprising twist to the story of astonishingly accurate
high-order balanced models. The papers have now appeared in
*J. Atmos. Sci.*
**64**, 1782-1793 and 1794-1810 (June 2007), and
reprints are available here.
The abovementioned
short paper in ADGEO includes
a brief summary of the hyperbalance equations
(.pdf, 0.16 Mbyte),
related in turn to a
discussion of the latest
examples of imbalance and inertia-gravity-wave radiation
-- Lighthill and non-Lighthill --
in
*J. Atmos. Sci.*
**66**, 1315-1326 (May 2009),
in the Special Collection on `Spontaneous Imbalance'.
The title is
*
Spontaneous imbalance and hybrid vortex-gravity
structures* (.pdf, 0.7 Mbyte,
© 2009 American Meteorological Society).

Here's the web version of
my 2005 lecture to the ECMWF Seminar,
*Some dynamics that is significant for chemistry*,
with tutorials on
the `polar stratospheric cloud roller coaster'
and
the gyroscopic pumping of the Brewer-Dobson circulation,
and a nod in the direction of
Michelson and Morley.

Here are two papers reporting
fundamental advances in wave-mean
interaction theory (work with Oliver Bühler,
*J. Fluid Mech* **492**, 207-230
and
*J. Fluid Mech* **534**, 67-95.
I am also
making available here the 1985 McIntyre-Palmer paper
justifying, via wave-mean interaction theory,
our fundamental definition of wave breaking
(pdf file, 0.9Mbyte),
and its
precursors in *Nature*
(1983, pdf file, 1.2Mbyte), in
*J. Atmos. Terrest. Phys*
(1984, pdf file, 1.4 Mbyte), and in
*J. Fluid Mech*.

Here's
the stratosphere's `gyroscopic pump' in action,
powered by the world's largest breaking waves.
This is the real stratosphere, remotely
observed from space! For more about gyroscopic pumping and its
significance,
see below --
also the major review in the Batchelor Millennium Volume
*Perspectives in Fluid Dynamics*
(Cambridge University Press), now reprinted
in paperback with
all corrections incorporated. I have run out of reprints but would
be glad to send a xerox copy to anyone who wants one. It tells how
three of the greatest atmospheric-science enigmas of the 20th century
were solved. The way they were solved beautifully illustrates
one of the grand themes of physics,
the
dynamical organization of fluctuations.

Here is
Rupert Ford's last published paper,
on imbalance and inertia-gravity-wave radiation
and written jointly with Warwick
Norton and myself.
A **Rupert Ford Memorial Fund** has been established;
for more information go to
this page
where also,
by kind courtesy of Professor E. David Ford,
Rupert's remarkable **PhD thesis** is now available as a
searchable pdf.

The related articles for the **Encyclopedia of
Atmospheric Sciences** are
here.

Here is the latest on air-sea interaction (fundamental fluid dynamics of wind-generated water waves).

Here's my *Plus Magazine* article on
tsunami waves
for the
Millennium Mathematics Project.

To see preprints of the McIntyre-Norton and Ford-McI-Norton papers
on potential-vorticity inversion and on the slow quasimanifold
and
Lighthill radiation
(which came out in the Millennium May Day issue of *J. Atmos. Sci.*),
click
here. There is a small but important
CORRIGENDUM here, also in *J. Atmos. Sci.*
**58**, 949,
15 April 2001.
The original 1996 report
with Roulstone on velocity splitting in Hamiltonian balanced models is
here.
The
review with Roulstone, in press for CUP and incorporating the
tutorial material from the 1996 report
(plus various updates and
a primer in Kähler and hyper-Kähler geometry)
is
now available here;
and preprints are still available on request.
Also shortly available will be
a preprint of the work with Mohebalhojeh on
*non*-Hamiltonian velocity splitting,
and a recent conference paper
(Limerick Symposium)
that tries to summarize our present knowledge of
balance and potential-vorticity inversion
and some still-outstanding mysteries.
This last link also leads to a beautiful
animated version of Figure 3 of the conference paper,
displaying
CRISTA data,
by kind courtesy of Dr Martin Riese of the University at Wuppertal.

A few reprints are still available, on request, of my review chapters
for *Meteorology at the Millennium*
(Academic Press and Royal Meteorological Society)
and for *Perspectives in Fluid Dynamics*
(Cambridge University Press), on the fluid-dynamical fundamentals of
large scale atmospheric circulations -- anti-friction and all that,
now out in paperback.
The *Meteorology* chapter was written more specifically for an
atmospheric-science audience; in addition, it
reviews the recent progress
in understanding the
**solar tachocline**
in the light of today's knowledge of
terrestrial stratospheric dynamics.

If you plan to buy the *Perspectives*
book (which has other interesting articles,
including Chris Garrett's ocean-dynamics review) or consult it in
a library, please remember that the wedges in my equations should be
read as crosses. They are vector products in 3D,
not (associative) exterior products. As far as I am aware, the equations are
otherwise correctly printed, but I'd be grateful to be told of any further
errors or obscurities
that come to light. *One further correction:* On page 621 I made a rash
statement about climate feedback, in which I missed the point that
this feedback could be radiatively compensated, through
changes in relative humidity. There is a
careful discussion in the recent review by Held and Soden (2000),
*Ann. Rev. En. Env.,* **25**, 441.)
**The corrections are all incorporated into the
paperback edition,**
and into most of the reprints I have distributed.

To find the
**polar cooling thought-experiment**,
click here (2.8K).
This is in section 6 of the review
`Atmospheric dynamics: some fundamentals, with observational
implications' written for the
*Proceedings of the International School of Physics
`Enrico Fermi',
CXV Course*, 1993.

For my anonymous ftp site (which has been mirrored on the web server)
click
here.
It holds mostly miscellaneous preprints, corrigenda
and reprints, including the `airsea' files (new ideas about wind-generated
water waves), and material for a book in preparation on
lucidity
and science (3.6K), related to the animation above. Comments welcome!
**NB**: some of the files
are compressed into the old Unix .Z format. These are
recognized, and can be uncompressed, by the standard utility
**gunzip**.

For the Campaign for Science and Engineering
(formerly Save British Science),
click
here,
and for related matters
here (7K)
and
here (5K).
The last two links point respectively to the celebrated Halloween Documents
and Eric S. Raymond's book *The Cathedral and the Bazaar*.
Between them they illustrate
why survival of the spirit of open science will continue to be socially and
commercially important, and how great will be our peril if we forget this.
It is this same spirit of open science, with its remarkable ideal and ethic
-- whose problem-solving power was discovered only a few centuries ago,
in Renaissance times -- that has made possible an astonishing achievement of
recent times: the development of complex yet reliable software, reliable
enough for vast systems like the Internet to function. The
Halloween Documents
testify to this in an unexpectedly cogent way.

Living organisms are more complex still. The Halloween Documents and related commentaries -- including the story of how the entire Internet nearly came under the control of a single giant corporation, in a parallel to World War Two -- have given us reason to hope that the spirit, ideal, and ethic of open science will sooner or later be recognized in the commercial, as well as in the academic, world as a prerequisite to the safety and reliability of -- for instance -- genetic engineering. Such recognition might help to turn the tide of madness in, for instance, patent law, arguably a major cause of technological hazard. See the important new book by Sulston and Ferry referenced there. This also gives us an insider's view of the human genome project.

Re further hope for the future (Grameen Bank etc), click here (2.9K). Re auditing, Goodhart's Law, and the Summerhill Affair, click here (10.9K).

**Back to the workaday present.**
Here's a link to my draft-revision toolkit,
lucidity-supplem.txt
(2.7K). Mainly for colleagues and students.

Here's
the web version of my lecture notes for
the Maths Methods III NST class on small oscillations and
group theory, including representation theory and character tables.
NST stands for the Cambridge *Natural Sciences Tripos*.
The notes (now with a logical slip on page 40 corrected) can be
downloaded as a pdf file (ca. 0.5Mbyte).
Here is the
first examples sheet for 2008,
and here is
the second.
Note that there's a **solution to sheet 2 q6** embedded in the
lecture notes, about halfway down page 80.

Some worked examples from past exams are here: 2003paper2q8.jpg, 2004paper2q7.jpg, 2004paper2q8.jpg, 2004paper2q9.jpg, 2004paper2q10.jpg, 2006paper2q9.jpg, 2006paper2q9.png (smaller file), 2006paper2q10.jpg, 2006paper2q10.png (smaller file), 2007paper2q8.jpg, 2007paper2q8.png (smaller file), 2007paper2q9.jpg, 2007paper2q9.png (smaller file), 2007paper2q10.jpg, 2007paper2q10.png (smaller file), 2006paper2q8-improved.jpg, 2006paper2q8-improved.png (smaller file). (In this last, under (ii), after showing that the 5 given elements are distinct an alternative is to consider the group they generate. That's easily shown to have order 9, another contradiction.)

The web version of my Part IB Fluid Dynamics lecture notes (Cambridge Mathematical Tripos, second year) is available here, and my graduate notes on Fundamentals of Atmosphere-Ocean Dynamics here.

I'm also making available some
supplementary materials from our annual Summer School in
Geophysical and Environmental Fluid Dynamics,
including notes on the
**`counterpropagating Rossby waves' mechanism**
underlying the commonest shear instabilities.
This unique two-week Summer School
was first held in September 1991, and then every year up to
September 2006. Throughout that time, it
attracted many lively graduate students and others
from all over the world.
I gave the core lectures on *Fundamental Concepts and Processes*.
After 2006 the Summer School was suspended, having suddenly lost
its financial support. To my great joy, however, it has now been
revived, for three years so far (September 2012-14),
as the Cambridge--École-Polytechnique
Summer School in Fluid Dynamics of Sustainability and the Environment.
Notwithstanding my advanced age I had the honour of contributing
guest lectures on two of these occasions.

Work in the Atmospheric Dynamics group has helped to explain, for instance, why the strongest ozone depletion occurs in the southern hemisphere, `even though' the chlorofluorocarbons and other chemicals causing it are emitted mainly in the northern hemisphere. This is a story of the epic journeys of atoms and molecules, circumnavigating the globe many times before arriving in the Antarctic polar stratosphere.

Understanding the atmosphere means understanding a nonlinear, multi-scale, chaotically-evolving fluid motion intimately coupled to radiative heat transport and chemistry. Data from modern terrestrial and space-based observing systems tell us a great deal about what happens; and the challenge is to understand why -- a prerequisite to predicting what will happen in future.

Some aspects of the problem are already well understood, but many challenges remain. We try to deploy all the means at our disposal -- mathematical theory, thinking by analogy, testing ideas with numerical experiments, comparison with data and, occasionally, experimentation on a small scale with real fluid-dynamical systems to which an idea under consideration applies. Something that thrills me personally is seeing, with the help of an appropriately general theory, how fluid phenomena you can easily observe in the kitchen sink [see The Quasi-Biennial Oscillation...] can, surprisingly, help to make sense of certain phenomena on the relatively grand scale of the entire atmosphere -- including three particular phenomena that used to be counted among the great enigmas of atmospheric science.

The first is the so-called `quasi-biennial oscillation' (QBO), observed since the early 1950s in the equatorial lower stratosphere, when the operational meteorological network became sufficiently developed. The east-west winds reverse direction roughly every fourteen months, throughout a belt encircling the globe, a remarkable example of order out of chaos and long-term predictability -- and regarding causal mechanisms a total enigma for nearly two decades, whose solution began to emerge only in the 1960s, when I was a graduate student. To see a beautiful laboratory analogue of the QBO (the Plumb-McEwan experiment), including an animated visualization, click here. (If you want to repeat the experiment, first read `Inside Stories'.)

The second phenomenon, and one-time enigma, is that of the extraordinarily low temperatures observed over the summer pole at altitudes just over 80 kilometres. Temperatures as low as 105 Kelvin (minus 168 Celsius) have been observed there -- far lower than anywhere else on, in, or above the Earth, despite the strong solar radiation incident on the summer pole. (Simple geometry shows this solar radiation to be stronger, in diurnal average, than anywhere else on Earth.)

The third phenomenon and, at first sight unrelated, enigma is what used to be called the turbulent `negative viscosity' due to large-scale eddies in the subtropical stratosphere and upper troposphere, and specifically recognized as enigmatic in Edward N. Lorenz' classic monograph `The Nature and Theory of the General Circulation of the Atmosphere', published in 1967 by the World Meteorological Organization in Geneva.

Despite gaps in our understanding we know, today, that all these
phenomena result from one basic type of fluid-dynamical process,
involving the dynamical organization of fluctuations.
This is the systematic, irreversible transport of angular momentum
that accompanies the
generation, propagation and dissipation of various kinds of internal
wave motion (whose *propagation mechanisms* organize the fluctuations,
in the manner reflected in the waves' polarization relations).
The waves in question depend on the gravitational
restoring force due to the strong stable stratification of the
atmosphere. They also, in many cases, depend on the Earth's
rotation as well. Wave-induced angular momentum transport
is a long-range process and has turned
out, in fact, to be a mechanism fundamental to the entire problem of
the global-scale circulation, and indeed, contrary to what is sometimes
thought, is the main cause of the circulation throughout altitudes
between about 10 and 100 kilometres, through a kind of global-scale
`gyroscopic pumping'.
In the wintertime stratosphere, for instance,
complicated, fluctuating fluid motions -- which
can be thought of as giant sideways-breaking waves --
conspire to push air persistently westward.
And when air is pushed westward
the Coriolis effect due to the Earth's rotation tries to
deflect it poleward.
So there is a systematic mechanical pumping action.
This drives what is called the `Brewer-Dobson circulation'.
With modern remote sensing, you can now
see the real gyroscopic pump in action!

The gyroscopic pumping pulls air gently but persistently upward and
poleward out of the tropical troposphere and lower stratosphere, then
pushes it back downward
toward the extratropical troposphere, the greater
part of it through the winter stratosphere via complicated, chaotic
pathways. The distinction between tropics and extratropics is, for
this purpose,
purely dynamical: the tropics feels the Earth's rotation far less.
Typical large-scale upwelling velocities in the tropical lower
stratosphere (altitudes 15 to 20 km) are seasonally variable roughly
from 0.2mm/s in northern summer to 0.4mm/s in northern winter, or
roughly 6 to 13 km per year, with the largest values confined mainly
to the most intense month or two of the northern winter.
This sets the *e*-folding timescale
for removal of chlorofluorocarbons from the troposphere,
because rates of land and ocean uptake of chlorofluorocarbons are at
least a decimal order of magnitude slower. This means that it would
take several centuries for chlorofluorocarbon concentrations
to diminish to 1 percent of their present values,
if all sources were somehow turned off tomorrow.
This same `Brewer-Dobson circulation'
plays a large part in determining the rate of
replenishment of stratospheric ozone, of the order of megatonnes
per day.

Wave breaking, understood in a suitably general sense that becomes apparent from theoretical studies of `wave-mean interaction', plays a crucial role in the wave-induced angular momentum transport. This in itself is a major challenge for theoreticians and numerical modellers. It means for one thing that the atmospheric circulation cannot be thought of as a simple turbulent fluid, to which classic turbulence theories and related concepts like Fickian `eddy diffusivity' or `eddy viscosity' might apply. Rather, the atmosphere viewed on almost any scale confronts us with a highly inhomogeneous, multi-scale `wave-turbulence jigsaw puzzle', in which wavelike and turbulent regions are often adjacent, and influence each other very strongly, and in which the net effect can often be `anti-frictional' -- tending to drive the system away from, not toward, solid rotation. Progress has depended, and will continue to depend, on clever combinations of theoretical thinking and computer modelling, all the way up to high-resolution numerical experiments run on the most powerful supercomputers. All this is very much part of the group's ongoing work under Professor Peter Haynes.

I have written a major review of the
fluid dynamical fundamentals, at early
graduate-student level, focusing on the three enigmas and
forming chapter 11, pp.557-624, of a new book *Perspectives in Fluid
Dynamics: A Collective Introduction to Current Research* edited by
G. K. Batchelor, H. K. Moffatt, and M. G. Worster. It was
published in hardback by Cambridge University Press in November 2000
and in paperback in January 2003.
[As
noted above, please kindly read
each *wedge* in the equations
as a (non-associative vector-product) *cross*;
I believe the printed formulae
are otherwise correct. I'd be glad to send a corrected copy to anyone
interested. The paperback edition incorporates these and a few other
corrections.]
The unifying theme is the fluid dynamics of
large scale atmospheric circulations, with a few remarks
on the opposite-extreme case of
the so called thermohaline, or meridional overturning,
circulation (MOC) of the oceans.

For more about the research group's work, especially in more recent years, see its publications pages.

*Note:* If you are interested in applying to do PhD work here
then you may want to look at
the relevant administrative information, which is available
here.
I'm now retired but
the work of the group continues under
Professor Peter Haynes,
and applications are encouraged from interested people with
good degrees in mathematics or physics. Some further information
is available on this site under
Courses and Opportunities.

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Emeritus Professor Michael Edgeworth McIntyre FRS (M.E.McIntyre at-sign damtp.cam.ac.uk, http://www.atm.damtp.cam.ac.uk/people/mem/), Centre for Atmospheric Science at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, UK. Tel +44-1223-337871, secretary -337870, fax -760419 and -765900