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Paul D. WilliamsAtmospheric, Oceanic and PlanetaryPhysics, Clarendon Laboratory, Oxford University

At first sight, the good old cup of tea hardlyseems a likely arena for performing ground-breaking science experiments. Indeed, in ahighly rigorous survey, 100% of the respon-dents (my four lab mates) said they wouldrather just drink the stuff than study it. Butthe events that take place in the averagecuppa are more exciting than most peoplerealise. Specifically, the tea currents in thecup can closely mimic, in microcosm, manyof the complex flow phenomena exhibitedby the earth’s atmosphere.

It turns out that there is a very intimateconnection between the fluid dynamics of afreshly stirred cup of tea, and those of anatmosphere on a rotating planet. It does notmatter that tea vortices are only a few centi-metres across, whereas typical atmosphericvortices can measure thousands of kilo-metres. The underlying balance of thephysical forces can be the same, and that isall it takes for the governing equations to bemathematically similar. So every time youstir a cup of tea (or coffee) you are running aminiature atmospheric simulation. Thisinvariance in the equations of motion iscalled ‘dynamical similarity’, and has beenknown about since at least the nineteenthcentury. It is a concept of great importanceto meteorologists, since it allows conclu-sions to be drawn about atmospheric phe-nomena by making observations of theanalogous flows in the laboratory.

Vettin (1884) was probably the first personto exploit dynamical similarity, by carryingout rotating laboratory experiments as ana-logues of atmospheres on rotating planets.He studied the surface flow in a rotating panof fluid with a lump of ice near the centre,representing a polar ice cap, and (to thescorn of many of his contemporaries) drewmeteorological conclusions from his results.

The main benefits of studying atmos-pheric flows indirectly in the laboratory arethat the system is under the completecontrol of the experimenter; that global

high-resolution measurements can be takensystematically; and that experiments can berepeated as many times as required. None ofthese statements hold when the atmos-phere is studied directly. Indeed, it seemsclear that we should not want to performexperiments on the real atmosphere, for fearof what the consequences might be if theexperiment goes wrong! Dynamical similari-ty allows us to conduct experiments onminiature ‘atmospheres’ in the laboratorywithout the many approximations of com-puter models; without the risks of tamper-ing with our climate system; and with aguarantee that our conclusions will be appli-cable to the real atmosphere so long as thedynamical similarity principle holds.

Following in the footsteps of Vettin andmany subsequent workers, I have spent thepast four years exploiting dynamical simi-larity to draw meteorological conclusions, in

pursuit of my DPhil. Admittedly, for practicalreasons, my experimentation vessel wasactually a bucket-sized steel cylinder ratherthan a teacup. I didn’t really use tea as theworking liquid either, but the principle isexactly the same. A photograph of the appa-ratus is shown in Fig. 1. The cylinder has adiameter of 25 cm and a depth of 25 cm. Asecond cylinder, of smaller diameter, hasbeen inserted at the centre of the maincylinder, for practical reasons, and the liquidrepresenting the atmosphere is the brightregion which fills the annular gap betweenthe two cylinders. The apparatus is mountedon a rotating turntable to mimic the rotationof the earth, and the tall metal frame sup-ports a video camera which views thesystem from about 2 m above.

The aim of the laboratory experiments hasbeen to investigate some of the propertiesof atmospheric waves. Existing high above

Storm in a teacup

Fig. 1 The laboratory ‘teacup’, as seen from above. The tank has a transparent glass base and lid. Bright whitelight illuminates the apparatus from below, and is received by a video camera above. The lid, in contact withthe liquid, is made to rotate under computer control relative to the turntable, which also rotates. This providesan instability from which Rossby-type waves can grow.

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our heads, these waves are much like oceanwaves, except that they are invisible to usbecause there is no well-defined surface atthe top of the atmosphere. The movementof atmospheric waves across the globecauses our weather, and so a detailed under-standing of how they operate is crucial inthe field of meteorology.

The main type of atmospheric wave,called a Rossby wave, is the prototype of thedisturbances that are responsible for theisobar patterns seen on weather forecastcharts. It brings with it warm and cold fronts,which cause sunshine and rain. But there is afar smaller and weaker class of wave, knownas an inertia-gravity wave, which propa-gates along with the Rossby wave. Theseweak inertia-gravity waves are not directlyresponsible for our weather, but they are stillable to have an influence on it by impactingupon the motion of the weather-carryingRossby wave. David and Goliath-style bat-tles are acted out high in the sky every day,in which the inertia-gravity waves attemptto interfere with the stronger Rossby wave,exchanging energy and momentum, andpotentially altering its speed and directionof travel. If they are successful, the rain thatwas originally headed for London might endup elsewhere.

From time to time, if the air is saturatedwith water vapour, the fluid motions asso-ciated with inertia-gravity waves can causelocal condensation, and then the wavesbecome visible to us as clouds. A stunningexample is the photograph shown in Fig. 2,

taken during the night in Kiruna, Sweden.The inertia-gravity waves tend to persist foraround 15 minutes before dissipating.Typically, gravity waves of wavelengths inthe range 5–50 km are visible from theground in noctilucent clouds on around onenight in three during the summer months,predominantly between latitudes 50 and70°N and between 2200 and 0400 local time(Dalin, personal communication).

One problem with weather-forecastingcomputer models is that they do not explic-itly take inertia-gravity waves into account,for reasons discussed by Lynch (2003). Theyare only represented implicitly, by using aparametrization of their expected effects onthe flow. Though inertia-gravity waveparametrizations, such as that proposed byHines (1997a, b), have undoubtedlyimproved the performance of forecastingmodels, they are still simply approximationswhich cannot possibly capture the fulldetails of the nonlinear interaction betweenRossby and inertia-gravity waves. The ques-tion that naturally arises is: is the missingpart of the interaction significant enough toaffect the reliability of numerical forecastingmodels? The answer has conventionallybeen thought to be ‘no’, although obtainingrigorous proof of this tacit assumption hasalways eluded researchers. Thanks todynamical similarity, it has recently becomepossible to obtain a more definitive answerin the laboratory.

Amazingly, it is possible to observe thecompeting inertia-gravity and Rossby waves

on a very small scale, in the laboratoryexperiment of Fig. 1. Experiments can beperformed in which groups of inertia-grav-ity waves develop in the vicinity of a strong,Rossby-like wave, and one can watch indetail what happens as they attempt toimpede its progress. The whole affair is cap-tured on videotape for subsequent analysis.A typical still from the video footage isshown in Fig. 3, clearly showing two groupsof inertia-gravity waves (one at ‘12 o’clock’and one at ‘6 o’clock’) co-existing with aRossby-like wave (responsible for the near-elliptical shape of the central blue-colouredregion). The flow visualisation techniquefirst described by Hart and Kittelman (1986)has been used to produce these colouredmaps of the waves. It is interesting to com-pare the inertia-gravity waves in the atmos-phere (Fig. 2) with those in the laboratory(Fig. 3). That waves on such dramatically dif-ferent scales (around a centimetre in thelaboratory and a few kilometres in theatmosphere) can appear so similar in form istestament to the power of dynamicalsimilarity.

We have performed over 200 hours ofexperiments using the laboratory appara-tus, and by carefully analysing the videotapes we have been able to come to conclu-sions about the circumstances under whichthe inertia-gravity waves appear, and thedynamical mechanisms by which they aregenerated. Such issues would have beenmuch more difficult to investigate by look-ing at the real atmosphere. Importantly, wewere also able to study the impacts of theinertia-gravity waves on the large-scalewave with which they coexist. We found thatthe inertia-gravity waves may be able tohave a significantly stronger impact thanhas previously been thought. There are cir-cumstances in which, via a phenomenonknown as stochastic resonance, the inertia-gravity waves can dramatically alter theprobability of a change from the stateshown in Fig. 3 to that shown in Fig. 4.Transitions such as this seem to occur muchmore readily in the presence of inertia-grav-ity waves than in their absence. Our findingsare backed up by computer simulations, andare described more fully in Williams et al.(2003).

Since time immemorial, fortune tellershave enchanted us with claims of ability topredict a person’s future. This has often beendone by studying the swirls in their cup oftea, as manifested by the shapes of tea-leafdeposits at the bottom of the cup. It is pleas-ing that the atmosphere’s fortunes can nowbe told in a similar fashion, and that the sci-entific basis (for this augury at least) issound. Cup of tea, anyone?

Fig. 2 Atmospheric inertia-gravity waves in the night sky. In this case, the waves are visible from the surfaceof the earth because they are travelling within a noctilucent cloud. Had the surrounding air not had such alarge water vapour content, condensation might not have occurred, and then the wave would haveremained invisible to the human eye and passed by unnoticed.

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AcknowledgementsThis article is based on a prize-winning entryin the New Scientist Wellcome Trust ScienceEssay Competition 2002. The work was car-ried out under a research studentship fromthe UK Natural Environment ResearchCouncil, held at the University of Oxford,with award reference numberGT04/1999/AS/0203. The author wishes tothank his supervisors, P. L. Read and T. W. N.Haine. The photograph in Fig. 2 was takenby Dr S. Kirkwood, Dr P. Dalin and Dr A.Moström of the Swedish Institute of SpacePhysics in Kiruna.

ReferencesHart, J. E. and Kittelman, S. (1986) Amethod for measuring interfacial wavefields in the laboratory. Geophys.Astrophys. Fluid Dyn., 36, pp. 179–185

Hines, C. O. (1997a) Doppler spreadparameterization of gravity wavemomentum deposition in the middleatmosphere. Part 1: Basic formulation.J. Atmos. Solar Terr. Phys., 59, pp. 371–386

––– (1997b) Doppler spread parameteri-zation of gravity wave momentumdeposition in the middle atmosphere. Part2: Broad and quasi monochromaticspectra and implementation. J. Atmos.Solar Terr. Phys., 59, pp. 387–400

Lynch, P. (2003) Margules’s tendencyequation and Richardson’s forecast.Weather, 58, pp. 186–193

Vettin, F. (1884) ExperimentelleDarstellung von Luftbewegungen unterdem Einfluss von Temperatur-Unterschieden und Rotations-Impulsen.Z. Meteorol., 1, pp. 227–230

Williams, P. D., Read, P. L. and Haine, T. W. N. (2003) Spontaneous generationand impact of inertia-gravity waves in astratified, two-layer shear flow. Geophys.Res. Lett., 30, p. 2255

Correspondence to: Dr P. D. Williams, NCASCentre for Global Atmospheric Modelling,Department of Meteorology, University ofReading, PO Box 243, Earley Gate, Reading RG6 6BB. e-mail: p.d.williams@reading.ac.uk

© Royal Meteorological Society, 2004.

doi: 10.1256/wea.152.03

Fig. 4 A second experimental image taken by the video camera. This time, there are three wavelengths of theRossby-like wave around the globe, as opposed to two in Fig. 3. Inertia-gravity waves seem to play animportant role in inducing transitions between states such as those shown in Figs. 3 and 4. Although theatmosphere explores a significantly more chaotic regime than is seen in the laboratory experiments, it seemslikely that atmospheric inertia-gravity waves might play a similar role in forcing local transitions.

Fig. 3 Experimental image taken by the video camera which views the apparatus in Fig. 1. The tank rotatesin the anticlockwise direction. The image can be interpreted by imagining that the North Pole is at the centre,and that the large outer circle represents the equator. A water–oil liquid fills the tank, and different colours inthis image correspond to different heights of the interface between the water and oil – blue corresponds to ahigh interface, and yellow to a low interface.