Profile of Keith Moffatt

PROFILE PROFILE Profile of Keith Moffatt Farooq Ahmed Science Writer Keith Moffatt was born in 1935 and raised field and obtained the spectrum of the mag- in Edinburgh, Scotland. He was four years netic fluctuations (2). The result would be old when his father left home to serve in verified experimentally nearly three decades the Second World War. “At that age, you later by French researchers, using liquid accept things,” Moffatt recalls. “It was a time gallium and an applied magnetic field (3). of great shortage. Everything in the UK was “The application that I had most in mind rationed—food, clothes, fuel, even sweets!” at that time,” Moffatt notes, “was in astro- The elder Moffatt, an accountant, had physics.” In the 1950s, dynamo theory, which introduced his son to mathematical games is the study of how the earth, stars, and other and arithmetic puzzles, and, when he re- heavenly bodies generate and maintain ’ turned at the war s end in 1945, recreational magnetic fields, was beset by conflicting mathematics recommenced. ideas. Furthermore, how these magnetic The early tutelage had a lasting effect: fields interacted with the interstellar medium ’ Keith Moffatt. Photo by Jill Paton-Walsh. Moffatt s facility with numbers would trans- and its turbulent ionized gases was poorly form into an aptitude for applied mathe- understood. matics and its use in fluid mechanics and helicity, but the result is there. He and I astrophysics. His contributions to our under- Knotted Vortices discovered it quite independently.” standing of magnetic and spin fields as well Toward the end of the 1960s, while teaching as his advocacy for the study of mathematics a course on magnetohydrodynamics, Moffatt Dynamos around the world have earned him fellow- identified an integral characteristic of fluid Helicity had immediate applications in dy- ships in the Royal Societies of both London flow that he named “helicity” (4), building on namo theory, and especially for the expla- ’ and Edinburgh. A 2005 recipient of the Royal the observations of two scientists working nation of the earth s magnetic field. About Society of London’s Hughes Medal, he serves nearly a century apart. halfway to the center of the earth, the mantle “ as an emeritus professor of mathematical “In 1869 Lord Kelvin recognized the fro- gives way to a liquid metal core, acon- physics at the University of Cambridge. He zen property of vortex lines in fluid flows, ducting fluid in random motion superposed ” was elected as a foreign associate of the and in 1958 Lodewijk Woltjer, an astro- on differential rotation, Moffatt explains. National Academy of Sciences in 2008. physicist then at the University of Chicago, This combination generates a magnetic field. He showed that dynamo action occurs even Magnetic Fields in a Turbulent Medium demonstrated the invariance of a puzzling integral quantity in the flow of a perfectly in a weakly conducting fluid, provided the Moffatt completed his undergraduate stud- conducting or Euler fluid. In struggling to fluid domain is large enough and the turbu- ies in mathematics at the University of ’ lence has an average nonzero helicity (6). Edinburgh. He left Scotland for Trinity find a physical interpretation of Woltjer s invariant, it dawned on me that there must While on a sabbatical at the Université College, Cambridge, in 1957, where he came Pierre et Marie Curie in Paris, Moffatt wrote under the influence of George Batchelor, be an analogous result for the nonlinear ” the first monograph on dynamo theory, in- an Australian fluid dynamicist. Batchelor set Euler equations. corporating helicity and its implications for Moffatt to work on his first research project Helicity, as Moffatt explains, represents the planetary and astrophysical dynamos (7). “By and played a decisive role in his career. degree of linkage or entanglement in a field thelate1970s,” he notes, “the basic principles “George was very sympathetic to students of vorticity, which can be thought of as the were well established, so the time was ripe for who came from outside Cambridge, as it had spin associated with a velocity field. Helicity ” is an invariant of the Euler equations, which such a book, which is still a standard in- been his own career path, Moffatt explains. ” In 1959 Batchelor founded the Depart- govern ideal, nonviscous flows. This concept troductory text. The publication led to an ment of Applied Mathematics and Theoreti- established a bridge between classical fluid explosion of activity in the field of dynamo cal Physics at Cambridge—a department that mechanics and topology, the study of shapes theory, with three other books on the subject counts in its ranks some of the world’smost and their continuous deformation. produced across the world within the next influential fluid dynamicists and theoretical Moffatt gives credit for the finding to Jean- five years. A massive computational effort physicists. He gave Moffatt a prepublication Jacques Moreau, now an emeritus professor throughout the 1980s and 1990s followed. draft of his paper on how turbulence inter- in Montpellier, France, who had found the Moffatt is currently working on an updated acts with temperature or a contaminant that same invariant several years before his pub- version of the monograph. does not influence the turbulence (1). lication (5). “As so often happens in our Two years later, Moffatt’s first paper in subject,” Moffatt explains, “someone else ’ This is a Profile of a recently elected member of the National 1961 extended Batchelor s ideas to the in- proved the concept in a paper that was Academy of Sciences to accompany the member’s Inaugural teraction of turbulence with a weak magnetic completely buried. Moreau didn’tcallit Article, 10.1073/pnas.1400277111. www.pnas.org/cgi/doi/10.1073/pnas.1400956111 PNAS Early Edition | 1of3 Downloaded by guest on September 24, 2021 Mathematical Sciences (AIMS), which was eventually founded in 2003 by former Cambridge mathematical physicist Neil Turok. Located in a suburb of Cape Town, the institute trains graduate students from across the continent. “The concept has worked extremely well,” notes Moffatt, “and has now expanded through the AIMS Next Einstein Initiative to three other loca- tions across Africa in Senegal, Ghana, and Cameroon.” Mathematics of Toys and Soap Films In recent years, Moffatt has worked with Japanese mathematician Yutaka Shimomura, Cambridge’s Tadashi Tokieda, and others on mechanical toys that exhibit puzzling behaviors: the Euler disk, which has a per- ceived finite-time singularity (16), the spin- ning hard-boiled egg with a friction-driven instability (17), and the rattleback, with a chiral instability and asymmetric behavior (18). Moffatt says the real interest in these problems is that they illustrate behavior that appears in complex fluid situations like the helicity-driven dynamo, or in the His Royal Highness Prince Philip visits the Newton Institute, October 1992. Keith Moffatt friction-driven instability of pressure-driven (Left) demonstrates the production of a cusp singularity at a free surface. Sir Michael Atiyah, flow in a 2D channel. Founder Director of the Institute (Right). Photo courtesy of MM Photographic. With Raymond Goldstein and Adriana Pesci at Cambridge, Moffatt worked on the problem of topological jumps in soap films Nearly thirty years elapsed before a major These efforts led Moffatt to consider what that span twisted wire loops. The researchers experiment carried out at the International happens when a knotted magnetic flux tube formed a one-sided Mobius-strip soap film Thermonuclear Experimental Reactor site in relaxes to a minimum energy configuration on a doubled-over loop of wire and found — Cadarache, France confirmed the basic ideas while conserving its knot topology a prob- that it jumps to a two-sided surface in mil- in Moffatt’s book (8). In the experiment, lem closely related to the pure mathematical liseconds at a critical moment when the wire a turbulent flow of liquid sodium driven question: What is the smallest length of rope is slowly untwisted (19). With the aid of by counter-rotating propellers produced of a fixed diameter needed to tie a given high-speed photography, they described “ ” dynamo action (9). More recently, physicists knot? (14). Thetheoryoftightknots, the detailed mechanism of this jump, and “ at the University of Chicago succeeded in Moffatt explains, has been considerably in the process opened up a new branch of creating knotted vortices in water using developed with applications in polymer topological fluid dynamics. ” “ physics and molecular biology (15). The Topologists, Moffatt notes, have been carefully fabricated hydrofoils (10). In his ” Inaugural Article, Moffatt recaps his inves- beauty of working in applied mathematics, studying minimal-surface area problems for he continues, “is that your results some- “ tigations into helicity and dynamo genera- more than a century, and this new work times turn out to have application in fields tion. He remarks that “it’s a good moment provides welcome interaction between pure far from your initial interests.” ” to talk about this work when theory meets mathematics and fluid dynamics. experiment!” (11). Newton Institute Musings In 1991 the British mathematician Sir Applying Mathematics Although he still performs research, Moffatt Michael Atiyah and others founded the Afterthreeyearsasprofessorofapplied retired from teaching in 2002. He recently Isaac Newton Institute for Mathematical built a personal Web site that chronicles mathematics at the University of Bristol, Sciences at Cambridge as a national visitor his life and career in applied mathe- Moffatt returned in 1980 to Cambridge, research center for the United Kingdom. matics. The site details his early life in where he has remained ever since as a pro- Moffatt ran one of the first programs, on Edinburgh during the war, and catalogs fessor of mathematical physics and a fellow dynamo theory, and succeeded Atiyah as major contributions, periods of sabbatical, of Trinity College.

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