Sir James Lighthill

He was a good piano player, and at Cambridge he met Nancy in a musical group, where she played the cello. All his life he and she made music together and with their friends. They were married in 1945when he was working at the National Physical Laboratory at Teddington on the mathematics of the design of aeroplane wings, and Nancy was working as a mathematician at the Royal Aircraft Establishment - RAE – at Farnborough. She was always a mathematical companion attending conferences with him and latterly sharing an office at University College Mathematics Department where she also taught.

Even by 1945 he had achieved success in research, which led to his award of a Fellowship at Trinity and then positions as Senior Lecturer and Beyer Professor at the University of Manchester at the age of 26 in succession to the great Sydney Goldstein. Through his own research and his inspired leadership, he established new directions in applied mathematics and theoretical fluid mechanics, and a great school - whose progeny have filled professorships around the world. There in Manchester James and Nancy's four eldest children were born and their family happily grew up together. James was often travelling down to London on long journeys by steam train. With his enormous powers of concentration, James used these journeys to develop his great mathematical theory of sound produced by the turbulent eddies in the very noisy exhausts of jet engines in those days, which were then just coming into passenger service.

There are perhaps three great strands in the legacy of James' fundamental research. First are the Lighthill approximations and asymptotic methods; to understand something of what these words mean, ask yourself, what is the percentage difference between a whole number, say 3, and another one that is greater by 2, say, 5. In this case the difference is 67%, but for two larger numbers such as 100 and 102, the difference is only 2%. So for larger numbers one can approximate N by N+2. Lighthill extended this thinking to the calculation of complicated flows around and within real objects, whether they were aeroplanes, swimming fish, or the ear. His approximations began by geometrical distortion. Looking at a rocket or an eel from far away is about the same as looking at a pencil or a piece of string, but looking very close to the nose of a rocket or of an eel, both look like the front of a football.

It was remarkable that 40 years ago, he could see that these transformations could lead to analysis and hand-calculations. Nowadays they form the basis for the computation of almost any kind of flow. He then showed how approximations to the exact equations for' the different parts of the flow, say near the fish or far away was the next step in the analytical simplification of the flow calculations. Professor Keith Stewartson and Frank Smith's pioneering work at University College analysing flows over the surface of aircraft wings using a three layer sandwich approach owes much to James' work.

The second strand of his innovations, that indeed he might not even recognise as such, came after he was appointed Director of the 8000 staff at RAE Farnborough in 1959 aged 35. These concerned the geometrical and topological aspect of flows which he explained in two commanding review essays on aeronautical fluid mechanics. They emerged from research into the shape of the Concorde wing, by the star team that included Dietrich Küchemann and other continental Europeans. It was necessary first to describe precisely the swirling flows over these triangular shaped wings. To a topologist a tea cup with a handle is the same as a ring doughnut, and a Concorde wing is the same as someone's head - because if they were rubber each could be stretched into the other. Identifying the crown points on a head of hair essentially defines the overall pattern; the same applies to flow patterns over wings. Of course topologists also think about what happens if you poke a hole into a round doughnut and turn it into a ring doughnut. James applied this thinking, of a multi-connected space, brilliantly to explain in the 1970s how the wings of tiny flies produce such a large lift. They first clap their wings together and then fling them apart. He enjoyed demonstrating this, with his arms behind his back, in the lecture room and at parties everywhere. But to return to RAE; like Isaac Newton, James' greatest predecessor as Lucasian Professor and also holder of a government job running the Mint, James also innovated in administration. One weekend he took the financial "books" home and on Monday morning, came back bringing instead of the usual scientific manuscript, just a new system for the accounts. A year or two later as I heard on a visit to the RAE, they were still trying to understand this approach. When I took up my job at the Met Office in the 1990s I reassured MOD that I would not emulate this approach. In fact we took on the Farnborough system which by then had settled down and was perhaps more Price-Waterhouse than Lighthill.

The third strand of his work was on waves - the subject of his magnum opus, and perhaps his greatest mathematical love. Last week's news of his final 9 hour swim in the waves, moved a French colleague to refer to 'la derniere vague'. As well as inventing an over arching theory for how sound waves are generated by turbulence, he developed the non-linear theory for how sound waves can be amplified to form noisy shock waves. He explained how atmospheric and water waves and even traffic waves convey energy and momentum from one place to another at speeds that are related to how they travel in groups - as you see when one group of white horses follows another on the ocean. This was the subject on which he lectured widely when he was the first and founding President of the Institute of Mathematics and its Applications.

This became his style. He believed more strongly than most scientists that his latest idea was really important and should be widely understood. However he was never complacent about his delivery of these lectures. Like a great actor he prepared his props - with the polychromatic hand written capitals on his transparencies - and he rehearsed them minutely, even out loud at 6 o'clock the morning before - as some bleary eyed colleagues who had been stay in adjoining rooms, noted recently at a conference breakfast. Nancy said this would not have happened if she had been there, which she usually was.

James' career after 1964 when he left RAE took him to Imperial College and the Physical Secretaryship of the Royal Society. He found new applications of mathematics and fluid mechanics to human and natural biology, especially in blood flow, hearing and swimming of fish and humans. He helped found the Physiological Flow Studies Unit at Imperial, headed by his friend Professor Caro. Both at the Royal Society and when he moved to the Lucasian Chair in Cambridge in 1969, he encouraged scientists and mathematicians to work with engineers on critical problems of industry and society, ranging from control of complex and large industrial systems to the renovation of urban housing.

At the Department of Applied Mathematics and Theoretical Physics, it was amusing to observe his expansive personality at the termly staff meetings chaired by the austere George Batchelor. They both shared the top table beneath the blackboard, with James Lighthill seated on the corner at least 4 feet away. But at this and other committees, where he was not in the chair, although he expressed his ideas strongly, he was always a loyal and constructive member of the team.

With this quality and his great intellect, he was an effective member and chairman of several top science and technology bodies dealing with major UK and international scientific and technological issues. Disappointingly for him the 1960s was a period when the UK had to scale down its ever more costly aerospace and other technological ambitions to a level that its very slowly growing economy could afford. Yet at the same time, the UK was not ready to participate fully in European wide projects, with the notable exception of Concorde. It has been suggested that this is why after RAE and the government decisions of the 1960s, James barely spoke about aerospace, even I gather in his family. But the reverse is not true! Aerospace scientists and engineers refer to his research everyday in their research. He really enjoyed and was much admired for his international work, whether as a speaker at conferences, or as after dinner speaker sometimes in the host's language whether Russian, French, German or more recently Portuguese. On committees he used his position to good effect, especially in enlarging the collaboration between mechanics and the other branches of science and engineering, such as when he was president of The International Union of Theoretical and Applied Mechanics and a member of the international and Royal Society/Royal Academy of Engineering Scientific Committees for the International Decade for Natural Disaster Reduction. His efforts led directly to better forecasts and new scientific understanding of tropical cyclones, with their immensely damaging winds, waves and floods.

His academic career ended on the highest possible note and great sense of personal fulfilment as Provost of University College from 1979-1989. He led as he did at Farnborough through total immersion in the essential business of the institution, namely its scholarship and education. He enthused and enlarged everyone working there, including those working in the vital administrative and fundraising tasks as well. At all social occasions he and Nancy added great life to the College. Naturally James also participated in a number of research projects of the College including the biomechanics of hearing and the fluid mechanics of oil platforms.

What a person and what a life! We are all fortunate to have been touched by the grandness of his life force and by his warmth. Perhaps we will be reminded of James in future when, like the widow in Charles Kingsley's Westward Ho, we hear the stones crashing and rolling on the beach and think of the group velocity of the waves bringing his energy, spirit and inspiration from somewhere far away.

THIS ADDRESS, BY PROFESSOR JULIAN HUNT FRS, UNIVERSITY OF CAMBRIDGE,
WAS GIVEN AT SIR JAMES' FUNERAL ON 27 JULY 1998

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