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James Lighthill’s legacy 10 years on

Lord Julian Hunt

Sir James Lighthill tragically died in August 1998 while swimming around the island of Sark - a repeat of his previous swim in the 1970s. He was 74 and still active in research and the promotion of international science, particularly its contributions to dealing with natural disasters. He was honoured posthumously with the Copley medal, the Royal Society’s highest award. With the founding of the Lighthill Institute of Mathematical Sciences (LIMS) 5 years ago at UCL, we are continually reminded of his great contributions to applied mathematics and how they still influence so much research today. His collected works are available at LIMS and in libraries (Hussaini 1997). James would have been very pleased, as the founding president of the Institute of Mathematics and its Application, by its close link with LIMS through our joint evening meetings at De Morgan House in Russell Square. The IMA’s London office is next to LIMS on the second floor of De Morgan House.

UCL, where he was Provost from 1979-1989, remembers him for visiting every part of the College, for championing interdisciplinary research and for his successes in battling with Whitehall. In this mellower period of his life he did not inflict on UCL a new accounting system, as he had done when he was youthful Director of the Royal Aircraft Establishment (RAE), Farnborough in his 1930s.  He helped lay the foundations for UCL’s position in the front rank of UK and even world universities. When James retired, he and his wife Nancy shared an office in the UCL Mathematics Department where he researched and taught.

Lighthill’s early papers on the analysis of nonlinear waves and vortex dynamics still provide the framework for studying these fundamentals of fluid dynamics, and also suggested  many applications to engineering and environmental problems. For example water flow in channels, traffic along roads and furthermore the behaviour of processes in complex systems generally tend to change quite suddenly depending on the ratio of speed of the flow (or other processes) to the speed of waves (or information) through the system. The Lighthill-Benjamin hydraulic theory of 1956 was recently applied by Klettner (a research student at UCL) and others to analyse the unexpected ways that, on arrival at a beach, some Tsunami waves cause the sea line to retreat before the wave breaks. This occurs when they are in the form of a depression rather than the usually depicted elevated wave (e.g. by the Japanese artist Hokusai).

The Lighthill-Whitham theory (1955) of traffic flow has, as we learned at a LIMS evening meeting recently, been verified in monitoring the waves (which move at about 25mph) of stop-start traffic on the M25. Modelling traffic flow, like any other random process nowadays, usually involves a continual dialogue between macroscopic theories (whether continuum or statistical) and computer simulation of large numbers of  individual  elements.

Two years before his death Lighthill gave a great lecture in Kyoto on tropical cyclones or hurricanes, in which he described a general theory bringing together the overall vortex dynamics, the energy from the condensing water vapour, and the generation of ocean  waves by the movement of the cyclones. He never left an opportunity to remind his audience about the important difference between phase speed and the group velocity of waves ---the theme of his IMA presidential address (which I heard as a research student in 1964).

He always wanted to demonstrate, but in different ways from those of Brooke Benjamin, his doppel-ganger in UK applied Mathematics, the power of classical analysis and physical insight in the solution of complex problems.

From the days when he was Director of RAE around 1960, Lighthill did not foresee or even encourage the extraordinary possibilities of numerical calculation, using electronic computers, in fields as diverse as fluid mechanics, physiology, or artificial intelligence. It was as if he saw this new approach as a competitor. By contrast Benjamin saw numerical computation as a complementary method for studying complex problems; mathematics uniquely provides insight and quantitative analysis into behaviour of systems that are effectively beyond the digital limitation of computers, just as they may be impossible to measure or simulate experimentally.

As well as the IMA his other institutional legacy was the Physiological Flow Studies Unit at Imperial College, which he set up with Colin Caro in 1966. The Unit continues as a world class centre for doctors, engineers and mathematicians researching into blood flow and related processes mainly in the human body. With Imperial College's merger with some of London’s leading hospitals the collaboration between the unit and medical practice has been greatly strengthened. He would have appreciated the application of their research on flow along the nasal passage coupled to work at UCL and Delft on the dynamics of vortices carrying small droplets. This provided evidence for the successful defence case in the recent murder trial of RV Jenkins in 2005.

Those of us who knew James Lighthill and worked with him were indeed privileged. But everyone can build on the foundations he laid, and continue to benefit from his papers and books. Also do not forget to view his remarkable film with Shon Ffowcs-Williams on Aerodynamic Sound. Don’t forget to laugh as well, when you see it. He would have expected you to do so.