-- to quote the late Hermann Bondi, an `opportunity to allow the bees in one's bonnet to buzz even more noisily than usual.'
What has this animation to do with communication skills, and with the public understanding of science? To find out, click here (17K). 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 on Magazine tab). STOP PRESS: pdf scans of Lucidity and Science Parts I and II are now available here.
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 lecture, 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. (It's a point that governments seem not to understand -- as with large IT systems like the proposed UK Home Office biometric ID-card database, which will cost many times what's promised and present an irresistible target for fraudsters, to say nothing of the Big Brother aspect and the criminalization of the innocent by programming error. Did I say `large IT systems'? The complex systems we're dealing with are the IT systems together with the humans using them -- very complex indeed.)
The Earth system is the mother of all complex systems but there's one simple, hard fact about it that needs wider recognition. And we scientists haven't pointed it out clearly enough until recently. That fact is independent of climate-model inadequacies.
On human timescales, the carbon dioxide we pump into the Earth system will stay there forever.
More precisely, the bulk of the carbon dioxide and other forms of `active carbon' -- including forms such as bicarbonate ions in the ocean and soils but excluding `passive' or mineralized carbon (coal, oil, kerogen, terrestrial limestone etc) -- will stay as active carbon in the Earth system for very many tens of thousands of years. For practical purposes, it's forever.
The evidence is overwhelming, with no dependence on
the big climate models used by IPCC. See for instance the
2005 Royal Society Policy Document on
ocean acidification, and the
clear discussion in
this open-access paper published in 2008
one of whose authors, David Archer,
has also published in 2009 a short
book
of outstanding accessibility as well as importance,
The Long Thaw: How Humans Are Changing the Next 100,000 Years
of Earth's Climate.
See especially pages 88-89 on the
PETM (the Paleocene-Eocene Thermal Maximum), also page 25 of
Challenged by Carbon
by Bryan Lovell, published early in 2010. Lovell's book
gives a more detailed account of the PETM and its far-reaching
implications, as seen by leading thinkers in the oil industry.
The evidence now to hand is a powerful and sober answer to all the
accusations of climate-model inadequacy and `climate alarmism'.
Fossil-fuel burning turns passive into active carbon,
irreversibly.
Unless we remove it the active carbon will stay forever
in the atmosphere, plants, soil, oceans, and ocean sediments,
all of them critical parts of our life support system.
Ways to slow the buildup of active carbon are set out in two
moreoutstanding books.
One is from an eminent scientist:
Sustainable Energy - Without the Hot Air
by David J. C. MacKay FRS,
free online at
http://withouthotair.com).
MacKay's book documents the numerical magnitudes and
makes it clear why, for instance, governments are
reckless to favour short-haul air travel over rail travel.
The other book is from an eminent economist:
Blueprint for a Safer Planet
by Nicholas Stern.
Lord Stern argues that
low-carbon economic growth is not only possible,
but also commercially attractive.
For more on the scientific background,
and on removing active carbon, I recommend
Fixing Climate:
What Past Climate Changes Reveal About the Current
Threat -- and How to Counter It
by Wallace S. Broecker ForMemRS and Robert Kunzig.
The main forum for serious debate is
the vast but valuable website
www.realclimate.org.
Some accusations of `climate alarmism' invoke the climate-model inadequacies as if that somehow justified inaction. Yes, the models are inadequate. And in particular they cannot tell whether today's active-carbon burden is, or is not, already enough to send the Earth system into a new Eocene, with sea level rising slowly but unstoppably to more than 200 feet higher than at present. It simply isn't known.
Did I say unstoppably? There's one and only one safe way to stop it. We
need to capture carbon dioxide and reconvert it to
passive carbon. Instead of tar-sand
canyons we could have mountains of gleaming white limestone and
dolomite.
Simple, doable, and quite a tourist attraction. Seriously,
take a look at
the
Royal Society report on geoengineering
of 1 September 2009, especially pages 15-16 (pdf pages 29-30).
Understanding the Sun is important too. Here's the latest on the solar tachocline. WHAT A ROLLER-COASTER RIDE! See third paragraph 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.
Here's a
first paper on turbulent mixing in the oceans,
in which generalized Paparella-Young `epsilon theorems' are
proved,
bearing on the `ocean conveyor belt' idea and why it's misleading
for some purposes.
This is a conference paper in press for
Turbulence in the Atmosphere and Oceans
(Proc. Intl. IUTAM/Newton Workshop held 8--12 December 2008,
ed. D. G. Dritschel, Springer-Verlag). A full report
incorporating further advances,
co-authored with
Francesco Paparella and William R. Young, is in preparation for the
Journal of Physical Oceanography.
A video of my IUTAM/Newton presentation
on this work, and on Lighthill theory, is available from the
Newton Institute website.
Here's a scan of my old (1989) paper
On dynamics and transport near the polar mesopause in
summer
(J. Geophys. Res.
94, 14617-14628, .pdf, 1.2Mbyte,
© 1969 American Geophysical Union)
which relates to the
Ellison-Britter-Osborn mixing efficiency formula that's also
part of the `conveyor belt' argument.
Here's a brief essay `On thinking probabilistically' (pdf, 0.2 Mbyte), now with all corrections before the presses rolled in October '07; the main correction to earlier versions is here. The essay was written for 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 why there's far more to all this than the old `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 recent Chapman Conference on Jets and Annular Structures in Geophysical Fluids prompts me to make available a scan of my 1970 paper bearing on the 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. 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). My 1993 potential-vorticity review, Isentropic distributions of potential vorticity and their relevance to tropical cyclone dynamics, is now available via this link. The jet sharpening ideas are developed further in a review 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 a new suggestion for Jupiter.
Basic to all 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 just out in vol. 15 of ADGEO (Advances in Geosciences), 2008, pp.47-56, gives a review of what's involved in such `catalysis', again pointing out the likely relevance to Jupiter. 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
preprint 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,
to appear with minor revisions in J. Atmos. Sci.
Its corollaries include a new nonlinear
stability theorem for shear flows.
For light relief, if you fancy it, here's my `geophysical' completion of Lewis Fry Richardson's famous turbulence ditty.
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 just out 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 --
now
in final form and
out in
J. Atmos. Sci.
66, 1315-1326,
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) and in J. Atmos. Terrest. Phys. (1984, pdf file, 1.4 Mbyte, can view with xpdf but prints best with acroread).
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 balance and Lighthill radiation and written jointly with Warwick Norton and myself. A Rupert Ford Memorial Fund has been established; for more information click here.
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 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 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 in electronic form.
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 wave' mechanism underlying the commonest shear instabilities. This unique two-week Summer School -- now sadly suspended owing to short-sighted cost-cutting -- 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.
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 `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 down 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, 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. 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.
Potential PhD students from the European Community should watch out: our research-studentship bureaucracy (which can help with tuition fees) has a rigid timetable such that you would need to contact us before mid-June. Possible start dates, under that particular bureaucracy, are restricted to October, November and December.
