## Obituaries: David G. Crighton

**November 21, 2000**

David G. Crighton, 1942-2000

David George Crighton was born in 1942 in Llandudno, where his parents had been moved to escape the bombing of London. His education took a remarkable change of direction in the lower sixth when a master observed that "Whatever else, he will never be any good at mathematics." Never fearful of a challenge, he abandoned A-levels in classics for double mathematics and physics. He entered St John's College, Cambridge, in 1961 and went down in 1964 with Firsts in Parts I and II of the Mathematical Tripos. He then made the conscious decision not to stay on for Part III but to accept a position teaching mathematics at Woolwich Polytechnic (now the University of Greenwich). There he taught a broad spectrum of mathematics for up to twenty-three hours a week and learned the techniques of crowd control (the evening class on subsidiary mathematics for engineering included several leather-clad, knife-bearing "mature students").

Then, by chance, he met John Ffowcs Williams, a reader in mathematics at Imperial College and an expert in aeroacoustics, and became his research assistant (at less than a quarter of the salary of a senior lecturer at Woolwich Polytechnic). His PhD at Imperial College followed in 1969; he remained there until 1974, when he was appointed a research associate in the Department of Engineering at Cambridge. He visited the department only once, however, as he was immediately---apparently out of the blue though in fact at the instigation of Sir James Lighthill---appointed professor of applied mathematics at the University of Leeds at the age of 32.

David immediately made a difference, motivating his colleagues, many of them older than himself, to become active in research, to raise research funds, and to take on students. He himself had 15 research students in his time at Leeds. When he had been there only about a year, a new research student asked if they could fix a time for a regular weekly meeting. David looked at his diary and said "How about Monday at 7 o'clock?" The student asked "a.m. or p.m.?" to which the reply was "Whichever you prefer." By 1986, when David left, the applied mathematics department at Leeds had risen to be one of the top three or four in the country, a position it retains to this day. David's spells as head of department, chairman of the School of Mathematics, and chairman of the Science Board (effectively dean) left indelible marks of his imagination, energy, and effectiveness.

These attributes continued to be the hallmarks of David's activities after he left Leeds, though now on a national and international scale. In 1986 he succeeded the late G.K. Batchelor as professor of applied mathematics at Cambridge, and he took over the headship of DAMTP in 1991. His tenure in this position was characterised by his fierce determination that the department should not only remain by far the strongest mathematical sciences department in Britain and Europe, but that it should rank at least equal with the much more generously funded departments in America.

He persuaded the university to create new chairs and attracted eminent scientists to fill them: By the summer of 1999, for example, the staff of the department included 15 fellows of the Royal Society, more than any other department in any other subject anywhere (and that does not count retired staff). The expanded department was very crowded, however, and David both had and implemented the vision of a new Centre for Mathematical Sciences, to house the whole Faculty of Mathematics. He and his colleagues have tirelessly raised almost all the necessary funds, mostly from private sources; the building is well under way, half the faculty has moved in, and the move will be complete in 2002.

All this activity was on top of David's work as chairman of many national and international committees (he succeeded Batchelor as chairman of the European Mechanics Committee and oversaw its transformation into a society, of which he was the first president); of his extensive editorial work (he succeeded Batchelor as editor-in-chief of the *Journal of Fluid Mechanics*, and he was editor of the *Cambridge Texts in Applied Mathematics* from 1986); and, since 1997, of his mastership of Jesus College, where he individually met all third-year undergraduates as well as staff and fellows.

Moreover, David Crighton had a full scientific career of his own, with one book and well over 100 published papers in major journals. His work can be categorised under four headings: (1) aero- and hydro-acoustics (sound generation by unsteady flow and turbulence and its scattering by rigid boundaries); (2) structural acoustics (in which the sound field in a fluid is coupled to vibration of embedded elastic structures); (3) propeller acoustics (sound generation by the specific flow phenomena associated with modern high-speed propellers); and (4) nonlinear acoustics (in which dissipative, not dispersive, mechanisms provide the balance for nonlinear deformations). All these topics have obvious applications in aircraft and marine engineering, and they are all further linked by Crighton's imaginative use of asymptotic methods to isolate and analyse the principal physical mechanisms underlying the phenomena of interest. His work in each of the four areas is briefly summarised here for readers of *SIAM News*:

(1) Pure Lighthill quadrupole turbulence radiation is often dominated by other mechanisms associated with the presence of solid boundaries. A highlight of Crighton's early work in this area, with F.G. Leppington, was the creative coupling of two sophisticated mathematical methods (the method of matched asymptotic expansions and the Wiener-Hopf technique) to analyse scattering by a semi-infinite plate of finite thickness [1]. The goal of all his work was to estimate the directivity of the generated or scattered sound, how its intensity scales with the speed of the bodies through the fluid and how it decays at long range. Sharp edges were shown to have a very strong (3/2-pole) far field. The interaction between sources, trailing edges, and downstream shear layers supporting large vortices were also shown to have stronger than expected acoustic enhancements in forward motion.

(2) In structural acoustics, Crighton was concerned with elucidating the crucial features of flow-structure interactions. He analysed the full near and far field of the Green's function for a fluid-loaded plate and found many distinct regions of physical and parameter space in which different mechanisms are dominant-a much more complex situation than had previously been supposed [2]. In much of his work on finite structures, Crighton identified new resonances that can be dominant in particular engineering applications. Proper analysis of the modes of vibration of a fluid-loaded ribbed plate, including previously neglected small terms, shows that the vibration decays much more slowly (algebraic rather than exponential decay) than indicated by previous theories [3]. Analysis of the effects of mean flow on forced structural response required extremely subtle use of the principle of causality, and showed that the system, although stable, could transfer energy from the mean flow into the driver of the forcing [4].

(3) The complexity of the flow generated by multibladed prop fans makes direct numerical simulation of the acoustic radiation virtually useless and puts a premium on sophisticated asymptotic analysis. A highly imaginative innovation of Crighton's was to consider a limit in which the number of blades is taken to be very large. For subsonic propellers, he discovered that the radiation is tip-dominated; when the blade tips are supersonic, however, the dominant source is at a radius at which the component of the flow velocity in the observer direction is sonic. Radiation actually decreases as the tip Mach number increases well above unity [5]. This trend agrees with experiment, but few predictions were able to capture it at the time. (4) Strong acoustic waves form shocks whose propagation can be followed by the well-known weak shock theory (WST), but in many cases this is not uniformly valid at large times or distances. Crighton's contributions to nonlinear acoustics were to investigate when and why WST fails. Dissipative sound waves of general geometry turn out to be governed by a generalised Burgers equation, which Crighton proved to be nonintegrable, except in the familiar plane wave case. It was necessary once more to analyse such waves asymptotically, and Crighton was able to find full details of the final "old-age" phase of the wave in both spherical and cylindrical geometries [6]. New nonlinear physical effects, such as supersaturation, were revealed. For cubically nonlinear waves, Crighton showed that "sonic shocks" can develop in a finite time and can subsequently dominate the large-time evolution of the wave [7]. Another inventive idea (in work with P.A. Blythe) was to analyse the dynamics of a reacting gas (combustion) by means of asymptotics based on the ratio of specific heats (gamma) being close to 1 [8].

David Crighton received many awards and honours, including fellowship of the Royal Society (1993), the AIAA Medal (1986), the Rayleigh Gold Medal of the Institute of Acoustics (1988), and three honorary doctorates (Crete, Manchester, and Loughborough).

Outside his work and his family, David's passion was music, especially opera. He was an authority on Wagner and wrote for an international magazine. He attended the Bayreuth Festival annually from his first visit, in 1962, as an undergraduate, until the onset of his illness. He held firmly to the view that there was only one thing better than a good performance of a favourite opera, and that was two good performances of that favourite opera or, as in the case of Pfitzner's Palestrina, which was performed at Covent Garden in 1997, all six good performances. A few weeks before his death he conducted his college orchestra in a performance of the Overture to Tannhäuser. Earlier, he had acted as sponsor in the West for the eminent Russian pianist Tatiana Nikolaeva, arranging for her to play at a concert in Cambridge to celebrate his own 50th birthday; he was once heard, in the middle of a weekday afternoon, giving a live Radio 3 interview about her.

What everyone remembers about David was his unique ability to combine tremendous hard work with wonderful warmth and good humour. While keeping all his parallel concerns clearly in his mind at the same time, and making hard decisions when necessary, he took a deep interest in every individual. He was widely admired and deeply loved and will be terribly missed. In 1969 he married Mary West, with whom he had two children. The marriage was dissolved in 1985, and in 1986 he married Johanna Hol. Johanna and his two children were with him when, on April 12, 2000, he lost the battle against cancer that he had been courageously fighting for over a year.

**References**

[1] D.G. Crighton and F.G. Leppington, *Singular perturbation methods in acoustics: Diffraction by a plate of finite thickness*, Proc. R. Soc. Lond. A., 335 (1973), 313-339.

[2] D.G. Crighton, *The Green function of an infinite fluid-loaded membrane*, J. Sound Vib., 86 (1983), 411-433.

[3] D.G. Crighton, *Transmission of energy down periodically ribbed fluid-loaded structures*, Proc. R. Soc. Lond. A., 394, 405-436.

[4] D.G. Crighton and J. Oswell, *Fluid loading with mean flow. I. Response of an elastic plate to localised excitation*, Phil Trans. R. Soc. Lond. A., 335 (1991), 557-592.

[5] D.G. Crighton and A.B. Parry, *Higher approximations in the asymptotic theory of propeller noise*, AIAAJ, 30 (1992), 23-28.

[6] J.J.C. Nimmo and D.G. Crighton, *Geometrical and diffusive effects in nonlinear acoustic propagation over large ranges*, Phil. Trans. R. Soc. Lond. A., 320 (1986), 1-35.

[7] I.P. Lee-Bapty and D.G. Crighton, *Nonlinear wave motion governed by the Modified Burgers Equation*, Phil. Trans. R. Soc. Lond. A., 323, 173-209.

[8] P.A. Blythe and D.G. Crighton, *Shock generated ignition: The induction zone*, Proc. R. Soc. Lond. A., 426, 189-209.

*T.J. Pedley, Department of Applied Mathematics and Theoretical Physics, Cambridge University. (Modified slightly and expanded from the obituary, by T.J. Pedley, that appeared in *The Guardian* in April.) *