# Obituaries: William Hill Reid

*SIAM Journal on Mathematical Analysis*from 1973 to 1981.

Bill was born on September 10, 1926, in Oakland, CA, to the late William MacDonald and Edna (Hill) Reid. He graduated from the University of California, Berkeley, in 1949 with a B.S. in electrical engineering, though his service as a U.S. Merchant Marine in the Pacific from 1945 to 1947 interrupted his undergraduate study. After receiving his M.S. from Berkeley in 1951, Bill embarked on his doctoral study at Cambridge University’s Trinity College, where he joined a group of young researchers and graduate students from all over the world doing research in the then-emerging field of turbulence. He studied the geometrical and statistical theories of isotropic turbulence under the direction of Ian Proudman.

In 1954, after completing his doctoral thesis at Cambridge and before formally receiving his Ph.D., Bill was drafted by the U.S. Army and spent the next two years at the Aberdeen Proving Ground in Maryland. While there he continued his scientific research “in between KP duty” and lectured at Johns Hopkins University, at the invitation of Stanley Corrsin. During this time, he also decided that there were no more theoretical advances he could help make in the field of turbulence. As Keith Stewartson, one of the most distinguished British applied mathematicians of his generation, once remarked in 1980, “Bill Reid’s work on isotropic turbulence dealt the field a body blow from which it never recovered.” Bill’s last paper on the subject, “Turbulent flow, theoretical aspects,” which he co-wrote with C. C. Lin, was published in *Handbuch der Physik* in 1963.

In 1958, Bill began his academic career at Brown University after spending the previous year as an NSF Postdoctoral Fellow at Yerkes Observatory in Williams Bay, WI. His interaction with Subrahmanyan Chandrasekhar at Yerkes marked the beginning of his work on hydrodynamic stability. In 1963, Bill was recruited to the University of Chicago with a joint appointment in the departments of mathematics and geophysical sciences. He spent the next 26 years at Chicago where he did much of his pioneering research in the stability of shear flows.

The analytical study of shear flow stability has a long and illustrious history, beginning with Werner Heisenberg’s 1924 doctoral thesis in which he attempted to find (for large values of the Reynolds number) asymptotic approximations to the solutions of the governing Orr-Sommerfeld equation. Subsequently, Heisenberg’s work was improved upon by W. Tollmien in 1929 and further clarified by C. C. Lin in 1944. These analyses all shared a significant limitation – the obtained approximations lacked uniformity, which in turn led to considerable controversy on the validity of their use in stability calculations. Lin himself was well aware of this limitation and devoted a great deal of effort to this problem in the 1960s. In a series of groundbreaking papers published in the 1970s, Bill developed a systematic approach to obtain uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation as well as to the eigenvalue relation used in stability calculations. More importantly, his work provided an elegant framework for attaining uniform asymptotic approximation to the solutions of a large class of higher-order ordinary differential equations of the hydrodynamic type, of which the Orr-Sommerfeld equation is an important example. Bill’s research also facilitated the development of the compound matrix method, now a widely-used shooting technique for the numerical solution of unstable eigenvalue and boundary value problems.

During his career, Bill published more than 70 research papers. His book, *Hydrodynamic Stability*, which he co-authored with the late P.G. Drazin of Bristol University in 1981, remains an authoritative classic of the subject.

Following his retirement from the University of Chicago in 1989, Bill accepted a position in the Department of Mathematical Sciences at Indiana University–Purdue University Indianapolis where he continued his teaching and research. He remained in Indianapolis until 2007, when he moved to Jacksonville, FL.

Bill is survived by his wife of 53 years, Elizabeth, and his daughter, Margaret F. Reid.