Michael James Lighthill (1924–1998)

mem-lighthill.qxp 9/23/99 4:02 PM Page 1226 Michael James Lighthill (1924–1998) David G. Crighton and T. J. Pedley mathematics almost as a throwaway for those who David G. Crighton like everything formalised, but in fact his style of James Lighthill was acknowledged throughout working was usually the reverse. the world as one of the great mathematical scien- In one of his most celebrated works, his first tists of this century. He was the prototypical ap- paper on “Sound generated aerodynamically” by plied mathematician, immersing himself thor- jet aircraft and the like, he developed the essen- oughly in the essence and even the detail of every tial mathematical structure completely in two engineering, physical, or biological problem he weeks, but felt that the users (aeroengine design- was seeking to illuminate with mathematical ers) would not be able to grasp the implications, description, formulating a sequence of clear math- and so he delayed submission of his manuscript ematical problems and attacking them with a for sixteen months, in which time he worked back- formidable range of techniques completely mas- wards from the conclusions, isolating the mean- tered, or adapted to the particular need, or newly ing at each stage—and refining and simplifying the created for the purpose, and then finally return- mathematics as he did so. ing to the original problem with understanding, pre- He was in no sense simply the deployer of ex- dictions, and advice for action. isting mathematics against a rich range of practi- His published legacy of six books and some cal problems. To be sure, his earliest papers on su- 150 papers (most of them republished in four vol- personic flight already showed brilliant mastery umes in 1997 by Oxford University Press) show at and exploitation of classical techniques. But much every stage a well-nigh perfect correspondence more powerful techniques were needed for prob- between a clearly identified physical process or lems such as those of how waves in fluids are gen- mechanism and its expression and description in erated and propagated, and for this Lighthill made mathematical terms. His papers or lectures often great developments in the theory of Fourier analy- emphasised the physical aspects and gave the sis, generalised functions, and asymptotics—all set out with elegance and economy, and full rigour, David G. Crighton is professor of applied mathematics at in a delightful 1958 book, Introduction to Fourier the University of Cambridge. His e-mail address is dgc@ damtp.cam.ac.uk. This segment is reprinted by permis- Analysis and Generalised Functions. Rather differ- sion of the author from The Independent, where it ap- ent ideas were needed for nonlinear problems, peared on July 22, 1998, following Lighthill’s death four such as the propagation and focusing of sonic days earlier. booms, and here Lighthill provided equally 1226 NOTICES OF THE AMS VOLUME 46, NUMBER 10 mem-lighthill.qxp 9/23/99 4:02 PM Page 1227 original and elegant new techniques, permanent of papers, and ap- and frequently used additions to the armoury. plications include Michael James Lighthill was born in Paris in kidney-stone- 1924 and excelled across the board at Winchester crushing before going up to Trinity College, Cambridge, in lithotripsy ma- 1941 for a two-year wartime B.A. He worked on su- chines and, with personic flight at the National Physical Labora- the same mathe- tory, Teddington, for the rest of the Second World matics, flood War, publishing his first paper before he was waves in rivers twenty. He then went as Senior Lecturer to Man- and traffic flow chester University at the age of twenty-two, before on highways. taking the Beyer Professorship of Applied Mathe- From Manches- matics there, aged twenty-six, in succession to ter, Lighthill went Sydney Goldstein. In his thirteen years at Man- on in 1959 to be- chester (1946–59) Lighthill ran one of the most come director of powerful and inventive fluid dynamics groups ever the Royal Aircraft formed anywhere. Establishment, He had many Ph.D. students who often rose to Farnborough, considerable heights themselves. Indeed, there where his leader- was a period in which no fewer than seventeen of ship extended to his Manchester students held chairs in the UK, the critical exam- Photograph courtesy of University College London. and that at a time when the number of universi- ination of every Sir James Lighthill ties was no more than a third of its present num- report emanating ber. Although prepared to share the credit on a from the RAE. The paper with a colleague, Lighthill almost never al- years 1959 to 1964 saw him again in his element lowed his name to appear as author on any paper (“Wouldn’t change it for anything!”), working on the wirtten by a student. And he was, then and since, aerodynamics of the slender delta wing for Con- tireless in his support for young scientists of any corde, on spacecraft, and on short-haul aircraft. He promise and for scientists working in disadvan- also worked with the post office in developing taged circumstances. commercial use of television and communications During these Manchester years Lighthill worked satellites while managing in unusual detail the extensively on gas dynamics, including effects im- work of the 8,000 RAE staff, of whom 1,400 were portant at very high speed, in his studies of ioni- professional scientists and engineers. Towards the sation processes and the diffraction of shock and end of his RAE time he became dissatisfied with blast waves. He also launched two major new fields the support in national societies for applied math- in fluid mechanics. The first of these, “aero- ematics and founded the Institute of Mathematics acoustics”, or “sound generated aerodynamically”, and Its Applications, of which he was the first was announced in a remarkable paper published president, in 1965–67. From 1964 to 1969 Lighthill by the Royal Society in 1952. Unusually but sig- held a Royal Society research professorship at Im- nificantly, that paper neither contains nor needs perial College, and here he began his great devel- so much as a single reference to any prior work. opment of mathematical biofluiddynamics: the This work has remained for nearly fifty years the quantitative understanding of the flow of blood in progenitor of all subsequent work in the field and mammalian cardiovascular systems, of air in the has been cited in many thousands of later papers. human airways, and of the flying of birds and in- It had immediate implication for noise reduction sects and the swimming of fish. Mastery of biol- in jet aeroengines, motivating the trend begun ogy was, he insisted, the sine qua non for entry into later in the 1950s and still continuing to engines this field. He revelled in lectures, not only in the with higher bypass ratio, greater diameter, and articulation of all the Latin names, but in his abil- lower exhaust speed, as mandated by Lighthill’s fa- ity to perform the appropriate gymnastics to mous eighth power law for jet noise. Remarkably, illustrate certain flying characteristics—in partic- the Lighthill theory was sufficiently versatile to be ular the “clap and fling” mechanism employed by applied also in problems as diverse as the heating the tiny wasp, Encarsia formosa, to endow it with of the Sun’s corona and the noise heard under a lift coefficient far above that obtainable from the water due to breaking surface waves and splash- ordinary aerodynamics in which the component ing drops. parts of the body do not break apart. The second new field, “nonlinear acoustics”, In 1969 he succeeded Paul Dirac, founder of was initiated by a famous 100-page article written much of quantum mechanics, in the Lucasian Pro- in 1956 in honour of the seventieth birthday of an- fessorship of Mathematics at Cambridge—though other great mechanics scientist, Geoffrey Taylor. when he referred to “my predecessor in the chair,” This field is now represented by many thousands one sensed he was thinking primarily of Newton. NOVEMBER 1999 NOTICES OF THE AMS 1227 mem-lighthill.qxp 9/23/99 4:02 PM Page 1228 Here he taught indefatigably and with enormous gusto six days of the week at nine in the morning. T. J. Pedley He widened his range yet further with work on con- It was during the fifteen years after he left the trol systems; on active control of sound, or anti- Royal Aircraft Establishment (1964–79), first as a sound; more and more on waves; on oceanography Royal Society Research Professor at Imperial Col- and atmospheric dynamics, including monsoon lege and then as Lucasian Professor of Mathemat- prediction and propagation; and on biological me- ics at Cambridge, that Lighthill totally transformed chanics at the microscopic level. the study of biological fluid dynamics. He wrote From 1979 to 1989 Lighthill was provost of major reviews of aquatic animal propulsion (1969), University College London, much engaged in fund- of animal flight (1974 and 1977), and of low raising; in new developments in the college, Reynolds number flagellar hydrodynamics (1976). particularly in the biology and biotechnology sides; Each of these is characterised by an exhaustive sur- and in dramatically improving the representation vey of the animal kingdom to make sure that all of women in senior posts. He still maintained his actual modes of locomotion are covered by the pre- scientific work with studies on the unpredictabil- liminary fluid dynamical analyses that he then ity of large systems, on wave energy extraction de- presents in qualitative if not quantitative forms. vices, and on features of the human auditory sys- (The lectures based on these surveys were always tem.

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