Scientists at the Isaac Newton Institute are spending six months trying to solve what Einstein dubbed the ultimate scientific problem - turbulence. Julian Hunt reports.

If you like to puzzle about the chaotic but recurrent patterns of motion in clouds or in the eddies in your saucepan of soup, you are in good company. Many famous physicists and mathematicians, including, it is said, Einstein, have remarked that turbulence is the ultimate problem they would turn to when everything else had been solved.

But of course mathematicians, engineers and physicists could not wait that long. Partly this is because turbulence is such a rich and rewarding field of research, but also because it plays a pivotal role in many natural phenomena and engineering systems.

In atmospheric turbulence, for example, gusts wreak havoc on people and buildings, but without the eddies to disperse it, atmospheric pollution would quickly become intolerable. Similar mechanisms operate in jet engines, where the controlled use of high level turbulence is essential in the design of efficient combustion chambers, but turbulence needs to be minimised in the exhaust to reduce noise.

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Over the past 40 years the fundamental understanding of turbulent flows has progressed considerably, first through theoretical studies, based on classical and novel uses of mathematics and fundamental physics (notably perturbation methods and dynamical systems), and second, through laboratory and field experiments in wind tunnels, the oceans and the atmosphere.

In my own career I have enjoyed all the aspects, from exploring how novel geometrical methods can be applied to turbulent flows, to observing turbulence in wind tunnels, water tanks, and from a 300-metre tower near the Rocky mountains.

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In the past 20 years, this research has become even more exciting with the use of ever faster and larger computers, now running at a million million operations a second. Not only can details of the three-dimensional dynamics be calculated, but with their brilliant images on the computer screen, it has become possible to visualise the real shapes of eddies, and how they form and break up in flows along a pipe or in a turbulent jet or in a thermally convecting system like the saucepan of soup.

Based on all these elements of fluid dynamics research, engineering design calculations of complex flows have become sufficiently reliable that they are tending to replace the traditional laboratory tests and full-scale trials, whether for constructing a new aircraft or a novel steel plant.

In the natural environment, governments now make decisions that affect everyone's lives on the basis of computer models, for example, for predicting how pollution is dispersed or, on the global scale, how climate will change as a result of chemical and physical changes in the atmosphere with turbulent mixing as the essential catalyst.

The work of many university research groups, including my own at the department of applied mathematics and theoretical physics at Cambridge, has found its way into such codes, through working with consulting companies, such as Cambridge Environmental Research Consultants Ltd, which I helped set up in 1986, and with government agencies and industry. I have also sat on the other side of the table as chief executive of the Meteorological Office.

However, because certain aspects of turbulence are still not understood, either qualitatively or quantitatively, some of these practical calculations are inevitably uncertain and need improvement. This is the focus of a six-month inquiry, coordinated by the Royal Academy of Engineering under the leadership of Geoff Hewitt of Imperial College, which is running at the Isaac Newton Institute for Mathematical Sciences at Cambridge between January and June 1999.

I have chaired the Scientific Advisory Committee. Through funding by leading UK industries and government agencies, the Engineering and Physical Sciences Research Council and private donations, more than 40 of the world's leading experts in the engineering, environmental and mathematical aspects of turbulence from Europe, Asia and the United States are participating in the programme of meetings and workshops.

The first objective is unusually philosophical for a scientific project: to explore the basic question of whether turbulence is the same wherever it occurs, by analogy with the universal laws governing the chaotic motion of gas molecules. Is turbulence near the wall of a pipe quite different from turbulence in the "bubbling" convective motion in the sun?

Studying this fundamental question is essential if engineers are to know more about the limitations of the computer codes they use. It should also assist them to select appropriate codes and equations to use for their various problems, and perhaps, to be sceptical about codes claiming to be valid for a very wide range of turbulent flow.

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However, the programme is mostly concerned with a number of particular problems of fundamental and practical importance:

* How is turbulence generated in an initially smooth flow, for example by the kind of external eddying motions caused by one set of rotor blades in a jet engine as they hit the surfaces of the downstream set of blades? We still need to understand more about Osborne Reynolds's original experiment, first performed in the 1880s, in which a dye stream in a pipe is suddenly dispersed as the flow becomes turbulent.

* What is going on inside the very small scale vortices in turbulence; how are they formed, and destroyed, and how do they collect together into larger vortices? Are they like "worms" threading through the flow, or like a rolled up sheet of newspaper, or are they much more random with rough "fractal-like" surfaces, like the surface of the moon? The answers to these geometrical and dynamical questions are needed to improve calculations on flames and about how chemicals mix and react together; as one of their engineers once put it: "ICI makes its money by bringing molecules together."

Meteorologists and chemical engineers have to predict how turbulence affects the way particles and droplets coalesce or break up in clouds and how droplets are dispersed in oil refinery processes. Calculations of certain mixing rates can vary by more than a factor of ten depending on the assumptions about the turbulence, an unacceptable level of error for practical purposes.

* Are the equations used in the "models" of turbulence reasonable from a mathematical point of view; for example, do they have an answer at all, only one answer, or even none at all? Sometimes computers "find" phantom solutions which do not really exist.

It is also essential to know whether the equations could be solved more effectively by different mathematical techniques. Because of the questions about these mathematical issues and also about computational methods, practitioners are often surprised by the results when computer codes are compared to data at "test-case" workshops.

The answers to the same equations for the same type of turbulent process often differ, especially if the experimental data are not made available before the tests are computed.

Several of the workshops within the INI programme are being jointly sponsored by the European Research Community for Flow Turbulence and Combustion (Ercoftac), the voluntary association that I helped my Continental colleagues to form in 1988. It brings together industrial, governmental and academic groups for the development and dissemination of research and advanced techniques, especially those in computational dynamics. There are now 150 institutions involved. Ercoftac has a number of special interest groups studying various topics in turbulence and a newly formed task group for evaluating quality and trust in computational fluid dynamics, including the use of turbulence models in computer codes.

The programme opened on January 11-12 with revealing reviews of the considerable uncertainties in calculating and understanding turbulence experienced by engineers and environmental experts in major industries and government agencies.

By the time we end in June we expect future projects of academic and industrial collaboration to have been set up based on progress during this programme including the grand challenge of deciding how best the next generation of super computer systems should be used to extract more of the secrets of turbulence.

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This should help in ensuring that our field of research will have access to these highly prized and still, in Europe, relatively scarce resources.