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THE BIZARRE contraption in Maarten Rutgers鈥� laboratory seems destined for a
museum of modern art. Up near the ceiling, a shiny metallic platform strapped
with Teflon-coated hoses holds a tank of soapy water. From there two long
strands of fishing line plunge down through the air. There鈥檚 not much more to
it.

It looks totally pointless until Rutgers flicks a switch and water begins to
trickle from the tank. Falling onto the lines, it races downwards, spreading
into an iridescent film and erupting into a magnificent raging river of
multicoloured swirls. At Ohio State University in Columbus, Rutgers has built a
machine to snare the beautiful beast called turbulence. And yet this isn鈥檛 the
usual collection of eddies and whorls you get when water gushes through a pipe,
or when a puff of smoke wanders into the annihilating headwind of a fan. In
Rutgers鈥� ultra-thin film, the beast has been squeezed into just two
dimensions鈥攖rapped in flatland.

That might appear pointless, too. But scientists are finding that the odd
habits of two-dimensional turbulence can also be seen in some impressive
three-dimensional realities, such as Jupiter鈥檚 Great Red Spot, and the immense
multi-headed vortices that swim through our oceans and alter our weather. So
Rutgers and other researchers are devising peculiar toys for stirring it up: not
only soap films, but salty oceans that rest on a tabletop and miniature planets
that hover in the lab.

Run a bath, then draw your hand through the water and you鈥檒l see the
essential character of turbulence: large swirls spawn little swirls. This
鈥渇orward cascade鈥� moves energy from bigger to smaller structures, eventually
shuttling it down to the smallest scales where it ends as the disorganised
molecular jostling called heat.

The Russian physicist Andrei Kolmogorov worked out an approximate theory for
this cascade half a century ago, and countless experiments have verified
it鈥攁s far as it goes. Where Kolmogorov鈥檚 theory falls down is in failing
to make sense of the wild fluctuations that occur sporadically in any turbulent
flow. So for want of any better theory, turbulence in three dimensions has
remained a scientific enigma.

It is not so enigmatic, however, when caged. In 1967, Robert Kraichnan, a
physicist at the US Office of Naval Research and once Einstein鈥檚 postdoc, worked
out how a turbulent fluid should behave if forced to live in just two
dimensions. He found, astonishingly, that the cascade should reverse itself.
Instead of breaking apart, small vortices should merge to form larger vortices,
leading not to microscopic mayhem but to huge, hurricane-like storms.

Kraichnan also went a long way towards predicting the mathematical details of
the result, such as the relative numbers of large and small swirls that should
occur in a typical setting. Ever since, physicists have been trying to put
Kraichnan鈥檚 predictions to the test.

You can鈥檛 build a two-dimensional wind tunnel, but in the mid-1980s, Yves
Couder of the Ecole Normale Sup茅rieure in Paris pointed out that a really
thin soap film would behave pretty much like a real flatland fluid. This idea
stimulated Mory Gharib, an aeronautical engineer at Caltech, to begin developing
the fine art of making a soap film flow. Other researchers followed suit. Hamid
Kellay, X. Wu and Y. Goldburg have been making bigger and swifter films at the
University of Pittsburgh. Rutgers learnt their technique as a postdoc there in
the mid-1990s, and went on to refine the geometry of these devices to produce
enormous, long-lasting soap films.

To force the fluid into two dimensions, the fishing lines in his device start
out close together at the top and gradually move farther apart below (see
Diagram). As the liquid falls, it clings to the lines and spreads into
a film just a few micrometres thick. Ordinary water would break up into a spray
of droplets, but the soapy surfactant makes the film elastic. It hangs together,
forming a liquid that lives in a mere sliver of space.

鈥淲e鈥檝e made films four storeys tall and four metres wide,鈥� says Rutgers, and
if someone had a bigger space to play with, there鈥檚 no reason that still huger
films shouldn鈥檛 be possible. For visual effect, the bigger the better, but when
it鈥檚 the physics you鈥檙e interested in, these enormous films run into trouble.
Friction between the film and the air spoils the simple two-dimensional
behaviour. So Rutgers works with a more modest film, just 2 or 3 metres high and
10 centimetres wide.

Stirring up a storm

As it rushes downhill, this liquid ribbon runs into a comb of tiny teeth.
Like boulders in a stream, they stir up a storm of turbulence. One of the
crucial advantages of Rutgers鈥� latest setup is the shape of the comb. Earlier
experiments used a single comb of teeth arranged across the channel, and
produced turbulence that died away鈥攏ot the ideal turbulence described by
Kraichnan. So Rutgers now uses two combs, arranged in an inverted V, a
combination that seems to produce authentic, persisting turbulence in
flatland.

So was Kraichnan right? The teeth churn up small swirls which move towards
the centre of the channel. There they encounter other small vortices and merge
into larger ones: this is the inverse cascade. And by bouncing a laser beam off
the film, Rutgers can precisely measure the velocities of the flow. As he
reported last year in Physical Review Letters (vol 81, p 2244), careful
mathematical analysis backs up Kraichnan鈥檚 more detailed predictions. The energy
of the moving liquid is distributed over swirls of various sizes in precisely
the way Kraichnan foresaw.

The experiment also verifies another of Kraichnan鈥檚 predictions. Look closely
at one of the large emerging swirls, and you鈥檒l find that it is actually made of
thousands of finely spaced spiral arms. Within the arms the fluid is rotating in
the same sense as the overall swirl, but between them it rebels, and rotates the
other way. As the vortex grows, these arms grow ever thinner and more numerous.
So while the naked eye sees the emergence of large vortices, the microscopic
view reveals an ever finer fracturing of the pattern of the liquid鈥檚 motion.
Rutgers is the first to have seen this dual pattern in his soap films, and to
prove beyond any doubt that flatland really works as Kraichnan said it
would.

But should we care? Does flatland physics have any consequences in the real
world? It seems that it does. In late 1997, for example, Patrick Tabeling and
Jerome Paret of the Ecole Normale Sup茅rieure in Paris saw the inverse
cascade in a box of turbulent saltwater鈥攐rdinary, three-dimensional
saltwater. Paret and Tabeling鈥檚 box is a 15-centimetre cube that contains two
distinct briny solutions: a lighter, less salty layer floating on top of a
dense, saltier one. Together, they are about 1000 times the thickness of
Rutgers鈥� soap film. But when the researchers stir things up, the layering has a
curious effect. As the lighter liquid wants to remain above the heavier, there
is a natural resistance to liquid movement up or down, and the solutions tend to
flow about within the layers. And sure enough, small vortices begin to gather
together until the container becomes one great swirl.

The same sort of stratification happens naturally in the Earth鈥檚 oceans and
atmosphere. 鈥淪tratification is quite enough to make a fluid act
two-dimensionally,鈥� says Phil Marcus of the geophysical fluid dynamics lab at
the University of California at Berkeley. And this effect is reinforced by the
Earth鈥檚 rotation. To see how, try standing on a spinning platform and throwing
an object straight out towards the edge. As you continue to turn with the
platform, the object will appear to swerve wickedly to one side, as if dragged
by some force.

On the spot

Something similar happens in the oceans and atmosphere. In particular, if a
small parcel of fluid tries to move up or down it feels these 鈥淐oriolis forces鈥�,
which tend to deflect it so that it moves parallel to the Earth鈥檚 surface. Over
the long haul, as fluids on Earth move over hundreds or thousands of kilometres,
their motion is largely two dimensional.

Knowing this led Marcus to suspect more than a decade ago that Kraichnan鈥檚
inverse cascade might have something to do with the more dramatic features of
planetary atmospheres. And not just on Earth. Atmospheric features don鈥檛 come
much more dramatic than the Great Red Spot on Jupiter. 鈥淭he continental United
States would fit inside it more than 200 times,鈥� says Marcus. The spot is
stable, too, having persisted since it was first sighted in 1610. It sits
between two jets of gas which race around Jupiter at different speeds. In
between, where they rub together, the jets stir up turbulence.

So is the Great Red Spot a two-dimensional turbulent vortex? According to
Marcus鈥檚 simulations, it is. In that region of his simulated planet, he says,
vortices spinning one way tend to gather together, while those spinning in the
opposite sense are repelled. The result is a conglomeration of thousands of
anticlockwise vortices into one large spot that looks a lot like the real
thing.

To put these ideas to a sterner test, Marcus approached experimental
physicist Harry Swinney and his colleagues at the University of Texas at Austin.
They bent a narrow trough of water into a ring and set it spinning. Pumping
fluid through the trough to create turbulence, they found that the rotation and
turbulence together made a pair of jets and then a vortex, which grew between
the jets and eventually filled the channel. It wasn鈥檛 red, but it certainly was
a great spot.

That was in 1988. Nowadays researchers are finding that two-dimensional
turbulence crops up closer to home, too. Edward Abraham of the National
Institute of Water and Atmospheric Research in Wellington, New Zealand, studies
the distribution of plankton in the ocean. Biologists and oceanographers would
expect plankton to be smoothly distributed, but instead populations are very
patchy.

Last year, Abraham noticed that plankton distributions have the same
mathematical profile as the swirls in two-dimensional turbulence. 鈥淭he
satellite images he showed were quite similar to the kind of thing we see,鈥� says
Rutgers. The ocean is turbulent, and presumably vortices carry the plankton into
large patches which, at the same time, have a wealth of subtle fine-scale
structure. It seems that flatland turbulence influences the ecology of the
organisms that lie at the foundation of the sea鈥檚 food web.

It even affects our weather. Water contains far more heat than the
atmosphere, so its movement has dramatic consequences for weather and climate:
when the Gulf Stream鈥檚 course across the North Atlantic changes, Europe鈥檚
farmers notice. Scientists are still a long way from pinning down all the
mechanisms by which heat moves around the planet, but turbulent vortices seem to
be crucial.

In 1993, for example, Phil Richardson of the Woods Hole Oceanographic
Institution in Massachusetts used data from underwater floats to make a census
of large vortices in the Atlantic. He found about a thousand of them, and they
were typically about 80 kilometres across. Some were single 鈥渕onopolar鈥�
vortices, slicing through the water like spinning Frisbees; others were
鈥渄ipolar鈥� vortices, two counter-rotating swirls moving as a pair. Both kinds can
shift immense amounts of heat from warm waters into colder regions of the
ocean.

Take 鈥渕eddies鈥�, for instance, the powerful vortices stirred up by water
flowing out of the Mediterranean. Although warm, this water is so salty that it
is denser than that of the Atlantic. It plunges 1000 metres down before
levelling off and flowing northwards as a warm underwater river off the coast of
Spain and Portugal. 鈥淗undred-kilometre pieces break off around 17 times each
year,鈥� says Richardson, 鈥渁nd these eddies drift off towards the southwest in the
Atlantic.鈥� Sometimes they last for five years or more and travel huge distances:
some researchers think that meddies can reach the Bahamas, having carried their
heat clear across the Atlantic.

At the University of Eindhoven in the Netherlands, GertJan van Heijst and his
colleagues are trying to catalogue the various types of vortex that are formed
in Kraichnan鈥檚 cascade. The researchers want to understand what makes these
vortices appear or go away, and what happens to all the energy they hold.
Because two-dimensional turbulence is the rule in the oceans, a basic
understanding of the vortices that it kicks up should help oceanographers to
unravel the myriad paths by which heat, salt and other substance move about.

At the moment, it is hard to see what the implications of Kraichnan鈥檚 theory
are for our oceans. The inverse cascade must help to make large vortices stable,
but no one has yet seen evidence of its precise mathematical form in the
distribution of vortex sizes. That鈥檚 not surprising鈥攖he ocean isn鈥檛
perfectly two-dimensional, and land masses have a habit of getting in the way.
So instead of solving equations, the researchers have to make model oceans.

Into a tank of stratified salt solution not unlike that used by Paret and
Tabeling, van Heijst and his colleagues inject pulses of extra solution from the
side. Each pulse creates turbulence, which to start with is three-dimensional.
But the swirling motion soon flattens out, and what usually emerges is either a
monopolar or a dipolar vortex, much like those Richardson counted in the
Atlantic. 鈥淭hese are like the elementary particles of two-dimensional
turbulence,鈥� says van Heijst. The researchers can also slam vortices into one
another. They tend to maintain their individuality, although sometimes two will
merge into one, or a dipolar vortex will split into two.

Along with the monopolar and dipolar vortices, van Heijst鈥檚 tank occasionally
produces a tripolar vortex, consisting of a single large vortex flanked two
smaller ones rotating in the opposite sense. This, too, has its counterpart in
the ocean. A spectacular example was observed by satellite in early January 1990
in the Bay of Biscay. An enormous vortex some 50 to 70 kilometres across
suddenly appeared, flanked by two smaller vortices to the north and south. The
whole thing lasted for a few days. 鈥淎s far as I know, this is the only clear
satellite picture of a tripole in the ocean,鈥� says van Heijst. 鈥淏ut monopolar
and dipolar vortices are abundant.鈥�

Having learnt so much by playing with fluids in flatland and its salty
analogues, why not go one step further and wrap flatland up into the surface of
a sphere? In his lab in Caltech, Gharib is planning to make a miniature planet
by levitating a rotating drop of water on a bed of sound waves. Who knows,
perhaps this pocket-sized planet will reveal the workings of our own curled-up
flatland.